Rotational Motion

236 questions · Physics · JEE Main

Rotational Motion

236 questions · Physics · JEE Main

Moment of inertia of a rod of mass ' M ' and length ' L ' about an axis passing through its center and normal to its length is ' $α$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross…2025 · 2 Apr · Shift 1 · Q55 · MCQ
A square Lamina OABC of length 10 cm is pivoted at ' $O^{'}$ . Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is : Includes diagram2025 · 2 Apr · Shift 1 · Q60 · MCQ
A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a… Includes diagram2025 · 2 Apr · Shift 1 · Q69 · MCQ
The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :2025 · 2 Apr · Shift 2 · Q51 · MCQ
A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 rad / s^{2}$ .… Includes diagram2025 · 2 Apr · Shift 2 · Q73 · Numerical
A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is Includes diagram2025 · 3 Apr · Shift 1 · Q61 · MCQ
Which of the following are correct expression for torque acting on a body? A. $τ = r \times L$ B. $τ = \frac{d}{d t} (r \times p)$ C. $τ = r \times \frac{d p}{d t}$ D. $τ = I α$ …2025 · 4 Apr · Shift 1 · Q58 · MCQ
If $L$ and $P$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $r = a (\hat{i} cos ω t + \hat{j} sin ω t)$ . The direction of force is2025 · 4 Apr · Shift 1 · Q68 · MCQ
A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\frac{x}{5}$ where $x =$ …2025 · 4 Apr · Shift 1 · Q71 · Numerical
A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $(ω_{1})$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no…2025 · 4 Apr · Shift 2 · Q71 · Numerical
$A, B$ and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. The moment of inertia of the given system about PQ axis is $\frac{x}{15} I$ … Includes diagram2025 · 7 Apr · Shift 1 · Q72 · Numerical
M and R be the mass and radius of a disc. A small disc of radius $R /3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis $A B$ passing through the centre $O$ … Includes diagram2025 · 7 Apr · Shift 2 · Q70 · Numerical
A rod of linear mass density 'λ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is.2025 · 8 Apr · Shift 2 · Q61 · MCQ
A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm . By applying an external torque of $25 π Nm$ for 40 s , the speed increases to 2100 rpm . The diameter of the disk is …2025 · 8 Apr · Shift 2 · Q72 · Numerical
A uniform circular disc of radius ' $R^{'}$ and mass ' $M^{'}$ is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius $R /2$ is removed from the… Includes diagram2025 · 22 Jan · Shift 1 · Q52 · MCQ
The position vectors of two 1 kg particles, (A) and (B), are given by $r_{A} = (α_{1} t^{2} \hat{i} + α_{2} t \hat{j} + α_{3} t \hat{k}) m and r_{B} = (β_{1} \hat{t} \hat{i} + β_{2} t^{2} \hat{j} + β_{3} t \hat{k}) m, respectively;$ …2025 · 22 Jan · Shift 1 · Q73 · Numerical
The torque due to the force $(2 \hat{i} + \hat{j} + 2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i} + \hat{j} + \hat{k})$ , would be2025 · 22 Jan · Shift 2 · Q53 · MCQ
A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length ' $L$ ' and makes an angle $3 0^{\circ}$ with the horizontal. The speed of the particle at the bottom of…2025 · 23 Jan · Shift 1 · Q58 · MCQ
A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $θ (t) = 5 t^{2} - 8 t$ , where $θ (t)$ is the angular position of the rotating…2025 · 23 Jan · Shift 2 · Q69 · MCQ
A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination $4 5^{\circ}$ . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be2025 · 24 Jan · Shift 1 · Q68 · MCQ
A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_{1}$ and $t_{2}$ , respectively, then2025 · 24 Jan · Shift 2 · Q62 · MCQ
A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :2025 · 24 Jan · Shift 2 · Q66 · MCQ
Two iron solid discs of negligible thickness have radii $R_{1}$ and $R_{2}$ and moment of intertia $I_{1}$ and $I_{2}$ , respectively. For $R_{2} = 2 R_{1}$ , the ratio of $I_{1}$ and $I_{2}$ would be $1/ x$ , where $x =$ .2025 · 28 Jan · Shift 1 · Q71 · Numerical
The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in…2025 · 28 Jan · Shift 1 · Q73 · Numerical
A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is2025 · 28 Jan · Shift 2 · Q52 · MCQ
The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $F = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in…2025 · 29 Jan · Shift 1 · Q69 · Numerical
A disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$ . It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is : Includes diagram2024 · 1 Feb · Shift 2 · Q80 · MCQ
A uniform rod $A B$ of mass $2 kg$ and length $30 cm$ at rest on a smooth horizontal surface. An impulse of force $0.2 Ns$ is applied to end B. The time taken by the rod to turn through at right angles will be…2024 · 1 Feb · Shift 2 · Q89 · Numerical
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$ . The sphere and the cylinder reaches upto maximum heights $h_{1}$ and $h_{2}$ respectively, above the initial level. The ratio $h_{1} : h_{2}$ …2024 · 4 Apr · Shift 1 · Q81 · Numerical
Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $A B$ as shown in figure is $8/ x$ . The value of $x$ is : Includes diagram2024 · 5 Apr · Shift 1 · Q64 · MCQ
A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$ . The value of $x$ is .2024 · 5 Apr · Shift 2 · Q84 · Numerical
Three balls of masses $2 kg, 4 kg$ and $6 kg$ respectively are arranged at centre of the edges of an equilateral triangle of side $2 m$ . The moment of inertia of the system about an axis through the…2024 · 6 Apr · Shift 2 · Q81 · Numerical
A thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $ω$ . If another disc of same dimensions…2024 · 8 Apr · Shift 2 · Q78 · MCQ
A circular table is rotating with an angular velocity of $ω rad / s$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $1 m$ … Includes diagram2024 · 8 Apr · Shift 2 · Q86 · Numerical
A string is wrapped around the rim of a wheel of moment of inertia $0.40 kgm^{2}$ and radius $10 cm$ . The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $40 N$ …2024 · 9 Apr · Shift 1 · Q88 · Numerical
A circular disc reaches from top to bottom of an inclined plane of length $l$ . When it slips down the plane, if takes $t s$ . When it rolls down the plane then it takes $(\frac{α}{2})^{1/2} t s$ ,…2024 · 9 Apr · Shift 2 · Q84 · Numerical
Four particles each of mass $1 kg$ are placed at four corners of a square of side $2 m$ . Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is $kgm^{2}$ … Includes diagram2024 · 27 Jan · Shift 1 · Q86 · Numerical
A heavy iron bar of weight $12 kg$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $6 0^{\circ}$ with the horizontal, the weight experienced by the man is :2024 · 27 Jan · Shift 2 · Q65 · MCQ
A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac{7}{x}$ , where $x$ is .2024 · 27 Jan · Shift 2 · Q84 · Numerical
A cylinder is rolling down on an inclined plane of inclination $6 0^{\circ}$ . It's acceleration during rolling down will be $\frac{x}{3} m / s^{2}$ , where $x =$ (use $g = 10 m / s^{2}$ ).2024 · 29 Jan · Shift 1 · Q82 · Numerical
A body of mass $5 kg$ moving with a uniform speed $32 ms^{- 1}$ in $X - Y$ plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be $kg m^{2} s^{- 1}$ …2024 · 29 Jan · Shift 2 · Q84 · Numerical
A particle of mass $m$ is projected with a velocity ' $u$ ' making an angle of $3 0^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its…2024 · 30 Jan · Shift 1 · Q64 · MCQ
Consider a Disc of mass $5 kg$ , radius $2 m$ , rotating with angular velocity of $10 rad / s$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating… Includes diagram2024 · 30 Jan · Shift 1 · Q87 · Numerical
Two discs of moment of inertia $I_{1} = 4 kg m^{2}$ and $I_{2} = 2 kg m^{2}$ , about their central axes & normal to their planes, rotating with angular speeds $10 rad / s$ & $4 rad / s$ …2024 · 30 Jan · Shift 2 · Q84 · Numerical
A body of mass ' $m$ ' is projected with a speed ' $u$ ' making an angle of $4 5^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{2 m u ^{3}}{X g}$ . The…2024 · 31 Jan · Shift 2 · Q82 · Numerical
Two identical spheres each of mass $2 kg$ and radius $50 cm$ are fixed at the ends of a light rod so that the separation between the centers is $150 cm$ . Then, moment of inertia of the system about an axis…2024 · 31 Jan · Shift 2 · Q85 · Numerical
A solid cylinder is released from rest from the top of an inclined plane of inclination $3 0^{\circ}$ and length $60 cm$ . If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is $ms^{- 1}$ … Includes diagram2023 · 1 Feb · Shift 1 · Q69 · Numerical
Moment of inertia of a disc of mass ' $M$ ' and radius ' $R$ ' about any of its diameter is $\frac{M R ^{2}}{4}$ . The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $\frac{x}{2}$ …2023 · 1 Feb · Shift 2 · Q69 · Numerical
Two identical solid spheres each of mass $2 kg$ and radii $10 cm$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40 cm$ . The moment of inertia of the system about…2023 · 6 Apr · Shift 1 · Q63 · Numerical
A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\frac{2}{x}$ . The…2023 · 6 Apr · Shift 2 · Q72 · Numerical
The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{x} MR^{2}$ , where $R$ is the radius and $M$ is the mass of the semicircular ring.…2023 · 8 Apr · Shift 1 · Q75 · Numerical
A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3 m / s$ (as shown in figure). Maximum height with respect to the initial position covered by it will be … Includes diagram2023 · 8 Apr · Shift 2 · Q64 · Numerical
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$ Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R : Fan…2023 · 10 Apr · Shift 2 · Q41 · MCQ
A force of $- P \hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2, - 3)$ is $P (a \hat{i} + b \hat{j})$ , The ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is -2023 · 10 Apr · Shift 2 · Q57 · Numerical
A solid sphere of mass $500 g$ and radius $5 cm$ is rotated about one of its diameter with angular speed of $10 rad s^{- 1}$ . If the moment of inertia of the sphere about its tangent is $x \times 1 0^{- 2}$ …2023 · 11 Apr · Shift 1 · Q72 · Numerical
A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $ω$ . A person sits at the center having two dumbbells in his hands. When he stretches…2023 · 11 Apr · Shift 2 · Q62 · Numerical
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is .2023 · 12 Apr · Shift 1 · Q62 · Numerical
A disc is rolling without slipping on a surface. The radius of the disc is $R$ . At $t = 0$ , the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its… Includes diagram2023 · 13 Apr · Shift 1 · Q54 · MCQ
A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $π : 22$ then, the value of its angular speed will be …2023 · 13 Apr · Shift 1 · Q71 · Numerical
A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be rad s $^{- 2}$ .2023 · 13 Apr · Shift 2 · Q64 · Numerical
A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $(k_{sph} : k_{cyl})$ is $2 : x$ . The…2023 · 15 Apr · Shift 1 · Q72 · Numerical
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $x$ cm. The value of $x$ is . Includes diagram2023 · 24 Jan · Shift 1 · Q67 · Numerical
A uniform solid cylinder with radius R and length L has moment of inertia I $_{1}$ , about the axis of the cylinder. A concentric solid cylinder of radius $R^{'} = \frac{R}{2}$ and length $L^{'} = \frac{L}{2}$ is carved out of the original cylinder. If…2023 · 24 Jan · Shift 2 · Q67 · Numerical
An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in… Includes diagram2023 · 25 Jan · Shift 1 · Q60 · MCQ
$I_{CM}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $I_{AB}$ is it's moment of inertia about an axis AB perpendicular to plane and… Includes diagram2023 · 25 Jan · Shift 1 · Q64 · Numerical
If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$ . The…2023 · 25 Jan · Shift 2 · Q71 · Numerical
A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ms $^{- 1}$ .2023 · 29 Jan · Shift 1 · Q67 · Numerical
A particle of mass 100 g is projected at time t = 0 with a speed 20 ms $^{- 1}$ at an angle 45 $^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2s… Includes diagram2023 · 29 Jan · Shift 2 · Q62 · Numerical
A thin uniform rod of length $2 m$ , cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $ω$ . If value of $ω$ in…2023 · 30 Jan · Shift 1 · Q63 · Numerical
A uniform disc of mass $0.5 kg$ and radius $r$ is projected with velocity $18 m / s$ at $t = 0$ s on a rough horizontal surface. It starts off with a purely sliding motion at $t = 0 s$ .… Includes diagram2023 · 30 Jan · Shift 2 · Q66 · Numerical
A solid sphere of mass $1 kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 1 0^{- 3} J$ . The speed of the centre of mass of the sphere is $cm s^{- 1}$ 2023 · 31 Jan · Shift 1 · Q69 · Numerical
Two discs of same mass and different radii are made of different materials such that their thicknesses are $1 cm$ and $0.5 cm$ respectively. The densities of materials are in the ratio $3 : 5$ . The moment of inertia of…2023 · 31 Jan · Shift 2 · Q69 · Numerical
A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to…2022 · 24 Jun · Shift 1 · Q69 · Numerical
A solid cylinder and a solid sphere, having same mass $M$ and radius $R$ , roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with…2022 · 25 Jul · Shift 1 · Q45 · MCQ
If force $F = 3 i + 4 j - 2 k$ acts on a particle position vector $2 i + j + 2 k$ then, the torque about the origin will be :2022 · 25 Jun · Shift 1 · Q47 · MCQ
Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows: I1 = M.I. of solid sphere about its diameter I2 = M.I. of solid cylinder about its axis I3 = M.I. of solid circular disc about its diameter I4 =…2022 · 25 Jun · Shift 2 · Q67 · Numerical
A disc of mass $1 kg$ and radius $R$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the…2022 · 26 Jul · Shift 1 · Q65 · Numerical
The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be $m$ . Given, the length of the rod is $103 m$ .2022 · 26 Jul · Shift 2 · Q59 · Numerical
A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads $-$ 1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be…2022 · 26 Jun · Shift 1 · Q46 · MCQ
A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is2022 · 26 Jun · Shift 2 · Q50 · MCQ
A pulley of radius $1.5 m$ is rotated about its axis by a force $F = (12 t - 3 t^{2}) N$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of…2022 · 27 Jul · Shift 1 · Q71 · Numerical
A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $4 ms^{- 1}$ ,… Includes diagram2022 · 27 Jul · Shift 2 · Q64 · Numerical
One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made…2022 · 27 Jun · Shift 2 · Q48 · MCQ
A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the… Includes diagram2022 · 27 Jun · Shift 2 · Q64 · Numerical
Four identical discs each of mass ' $M$ ' and diameter ' $a$ ' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $OO^{'}$ is $\frac{x}{4} Ma^{2}$ . Then,… Includes diagram2022 · 28 Jul · Shift 1 · Q70 · Numerical
Match List-I with List-II Choose the correct answer from the options given below : Includes table2022 · 28 Jun · Shift 1 · Q46 · MCQ
The position vector of 1 kg object is $r = (3 i - j) m$ and its velocity $v = (3 j + k) m s^{- 1}$ . The magnitude of its angular momentum…2022 · 28 Jun · Shift 1 · Q64 · Numerical
A ball is spun with angular acceleration $α$ = 6t2 $-$ 2t where t is in second and $α$ is in rads $-$ 2. At t = 0, the ball has angular velocity of 10 rads $-$ 1 and angular position of 4 rad. The most appropriate expression for…2022 · 28 Jun · Shift 2 · Q51 · MCQ
A $34$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ef and Fw are the reaction forces of the floor and the wall, then ratio of $F_{w} / F_{f}$ … Includes diagram2022 · 28 Jun · Shift 2 · Q53 · MCQ
A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the… Includes diagram2022 · 28 Jun · Shift 2 · Q76 · Numerical
The torque of a force $5 \hat{i} + 3 \hat{j} - 7 \hat{k}$ about the origin is $τ$ . If the force acts on a particle whose position vector is $2 i + 2 j + k$ , then the value of $τ$ will be2022 · 29 Jul · Shift 2 · Q58 · MCQ
A spherical shell of 1 kg mass and radius R is rolling with angular speed $ω$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is $\frac{a}{3}$ R2 $ω$ . The value of a… Includes diagram2022 · 29 Jun · Shift 1 · Q44 · MCQ
The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If $\frac{I _{1}}{I _{2}}$ is ${{x{\pi ^2}} \over…2022 · 29 Jun · Shift 2 · Q68 · Numerical
Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the… Includes diagram2022 · 30 Jun · Shift 1 · Q61 · Numerical
A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, ignoring the friction due to clamping at its lower…2021 · 1 Sep · Shift 2 · Q73 · Numerical
Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around is periphery as shown in the… Includes diagram2021 · 16 Mar · Shift 1 · Q65 · Numerical
Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $P$ of magnitude 100 N is applied at point A of the frame. Suppose the force is $P$ resolved… Includes diagram2021 · 16 Mar · Shift 1 · Q71 · Numerical
A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $θ$ with the horizontal. The acceleration of the disc will be $\frac{2}{b}$ g sin $θ$ where b is .… Includes diagram2021 · 16 Mar · Shift 2 · Q62 · Numerical
A force $F$ = $4 i + 3 j + 4 k$ is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is . (Round off…2021 · 16 Mar · Shift 2 · Q70 · Numerical
A triangular plate is shown. A force $F$ = 4 $i -$ 3 $j$ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are : Includes diagram2021 · 17 Mar · Shift 1 · Q48 · MCQ
A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular… Includes diagram2021 · 17 Mar · Shift 1 · Q51 · MCQ
The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is . (Assuming the acceleration to be uniform).2021 · 17 Mar · Shift 1 · Q63 · Numerical
The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach… Includes diagram2021 · 17 Mar · Shift 1 · Q65 · Numerical
A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30 $^{\circ}$ with the horizontal plane, without slipping. How long will the sphere take to return to the… Includes diagram2021 · 17 Mar · Shift 2 · Q52 · MCQ
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $ω$ . Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :2021 · 18 Mar · Shift 1 · Q50 · MCQ
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is :2021 · 18 Mar · Shift 2 · Q51 · MCQ
A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is : [The coefficient of… Includes diagram2021 · 18 Mar · Shift 2 · Q55 · MCQ
A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't1'. When it rolls down the plane, it takes time t2. The value of $\frac{t _{2}}{t _{1}}$ is $\sqrt {{3 \over…2021 · 20 Jul · Shift 1 · Q67 · Numerical
A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :2021 · 20 Jul · Shift 2 · Q56 · MCQ
Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to…2021 · 20 Jul · Shift 2 · Q67 · Numerical
A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is .2021 · 20 Jul · Shift 2 · Q72 · Numerical
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this…2021 · 22 Jul · Shift 2 · Q51 · MCQ
The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed $x v_{0}$ . Then the value of x is .2021 · 22 Jul · Shift 2 · Q73 · Numerical
Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I1 = M.I. of thin circular ring about its diameter, I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre, I3 =…2021 · 24 Feb · Shift 1 · Q62 · MCQ
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is $\times$ …2021 · 24 Feb · Shift 2 · Q68 · Numerical
A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $θ$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel? Includes diagram2021 · 25 Feb · Shift 2 · Q51 · MCQ
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis…2021 · 25 Jul · Shift 1 · Q47 · MCQ
A particle of mass 'm' is moving in time 't' on a trajectory given by $r = 10 α t^{2} i + 5 β (t - 5) j$ Where $α$ and $β$ are dimensional constants. The angular momentum of the particle…2021 · 25 Jul · Shift 1 · Q71 · Numerical
A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s…2021 · 25 Jul · Shift 2 · Q70 · Numerical
Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket… Includes diagram2021 · 26 Aug · Shift 1 · Q70 · Numerical
The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m2. Includes diagram2021 · 26 Aug · Shift 2 · Q54 · MCQ
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to…2021 · 26 Feb · Shift 1 · Q46 · MCQ
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a…2021 · 26 Feb · Shift 2 · Q63 · MCQ
Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :2021 · 27 Aug · Shift 1 · Q49 · MCQ
Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $ω$ 1 and $ω$ 2 respectively and are brought into contact…2021 · 27 Aug · Shift 2 · Q45 · MCQ
Choose the correct answer from the options given below: Includes table2021 · 27 Jul · Shift 1 · Q51 · MCQ
The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is $⊥$ to the plane of the disc and passing through its centre) of… Includes diagram2021 · 27 Jul · Shift 1 · Q55 · MCQ
In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $(\frac{I _{1}}{I _{2}})$ will… Includes diagram2021 · 27 Jul · Shift 2 · Q63 · Numerical
Angular momentum of a single particle moving with constant speed along circular path :2021 · 31 Aug · Shift 1 · Q60 · MCQ
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis…2021 · 31 Aug · Shift 2 · Q45 · MCQ
A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The… Includes diagram2020 · 2 Sep · Shift 1 · Q48 · MCQ
Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm… Includes diagram2020 · 2 Sep · Shift 1 · Q49 · MCQ
Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg-m2 and 10 rad s–1 respectively…2020 · 2 Sep · Shift 2 · Q46 · MCQ
A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational…2020 · 3 Sep · Shift 1 · Q45 · Numerical
Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is I = $M (\frac{R ^{2}}{4} + \frac{L ^{2}}{12})$ . If such a…2020 · 3 Sep · Shift 1 · Q63 · MCQ
An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $\frac{N}{20}$ … Includes diagram2020 · 3 Sep · Shift 2 · Q41 · Numerical
A uniform rod of length ‘ $l$ ’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $ω$ the rod makes an angle $θ$ with it (see figure). To find $θ$ equate the rate… Includes diagram2020 · 3 Sep · Shift 2 · Q57 · MCQ
ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If… Includes diagram2020 · 4 Sep · Shift 1 · Q60 · Numerical
A circular disc of mass M and radius R is rotating about its axis with angular speed $ω_{1}$ . If another stationary disc having radius $\frac{R}{2}$ and same mass M is droped co-axially on to the rotating disc. Gradually both discs…2020 · 4 Sep · Shift 1 · Q62 · Numerical
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is : Includes diagram2020 · 4 Sep · Shift 2 · Q47 · MCQ
Consider two uniform discs of the same thickness and different radii R1 = R and R2 = $α$ R made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the…2020 · 4 Sep · Shift 2 · Q55 · MCQ
A force $F = (i + 2 j + 3 k)$ N acts at a point $(4 i + 3 j - k)$ m. Then the magnitude of torque about the point $(i + 2 j + k)$ …2020 · 5 Sep · Shift 1 · Q43 · Numerical
A wheel is rotating freely with an angular speed $ω$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled…2020 · 5 Sep · Shift 1 · Q51 · MCQ
A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most… Includes diagram2020 · 5 Sep · Shift 2 · Q45 · Numerical
A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T1 and, (ii) back and forth in a direction perpendicular to its plane, with a period T2. The ratio $\frac{T _{1}}{T _{2}}$ will…2020 · 5 Sep · Shift 2 · Q52 · MCQ
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is : Includes diagram2020 · 6 Sep · Shift 1 · Q50 · MCQ
Four point masses, each of mass m, are fixed at the corners of a square of side $l$ . The square is rotating with angular frequency $ω$ , about an axis passing through one of the corners of the square and parallel to its diagonal, as… Includes diagram2020 · 6 Sep · Shift 1 · Q55 · MCQ
The linear mass density of a thin rod AB of length L varies from A to B as $λ (x) = λ_{0} (1 + \frac{x}{L})$ , where x is the distance from A. If M is the mass of the rod then its moment of inertia…2020 · 6 Sep · Shift 2 · Q37 · MCQ
As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance… Includes diagram2020 · 7 Jan · Shift 1 · Q51 · MCQ
The radius of gyration of a uniform rod of length $l$ , about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod, and perpendicular to it, is :2020 · 7 Jan · Shift 1 · Q59 · MCQ
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $μ$ = 0.4, the maximum possible value… Includes diagram2020 · 7 Jan · Shift 2 · Q39 · Numerical
Mass per unit area of a circular disc of radius $a$ depends on the distance r from its centre as $σ (r)$ = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and assing through its…2020 · 7 Jan · Shift 2 · Q57 · MCQ
Consider a uniform rod of mass M = 4m and length $ℓ$ pivoted about its centre. A mass m moving with velocity v making angle $θ = \frac{π}{4}$ to the rod's long axis collides with one end of the rod and sticks to it. The angular…2020 · 8 Jan · Shift 1 · Q43 · MCQ
A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :2020 · 8 Jan · Shift 2 · Q42 · MCQ
A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s–1) with which it can be rotated about its other end in space station is : (Breaking stress of wire = 4.8 × 107 Nm–2 and area of…2020 · 9 Jan · Shift 1 · Q45 · Numerical
One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30º from the horizontal (see figure). Its angular speed when it hits the table is given as $n$ s-1, where n is… Includes diagram2020 · 9 Jan · Shift 1 · Q47 · Numerical
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I0/IA of moment of inertia I0 of the system about an axis passing… Includes diagram2020 · 9 Jan · Shift 1 · Q49 · MCQ
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1 and m2 (m1 $>$ m2) are attached to the ends of the… Includes diagram2020 · 9 Jan · Shift 2 · Q50 · MCQ
A thin circular plate of mass M and radius R has its density varying as $ρ$ (r) = $ρ$ 0r with $ρ$ 0 as constant and r is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the…2019 · 8 Apr · Shift 1 · Q62 · MCQ
An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular…2019 · 8 Apr · Shift 2 · Q47 · MCQ
A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time t = 0.01s, remaining essentially horizontal. The angle… Includes diagram2019 · 8 Apr · Shift 2 · Q60 · MCQ
A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the incline. The ratio hsph/hcyl… Includes diagram2019 · 8 Apr · Shift 2 · Q68 · MCQ
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $θ$ , where $θ$ is the angle by which it has rotated, is given as k $θ$ 2. If its moment of…2019 · 9 Apr · Shift 1 · Q52 · MCQ
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane. : (i) a ring of radius R, (ii) a solid cylinder of radius R/2 and (iii) a solid sphere of radius R/4 . If in each case, the speed…2019 · 9 Apr · Shift 1 · Q54 · MCQ
A thin smooth rod of length L and mass M is rotating freely with angular speed $ω$ 0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod…2019 · 9 Apr · Shift 2 · Q43 · MCQ
Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular accleration of 20 rad/s2 must be applied about the axis for a duration of :-2019 · 9 Apr · Shift 2 · Q60 · MCQ
If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :2019 · 9 Jan · Shift 1 · Q54 · MCQ
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is $θ$ , thrown : Includes diagram2019 · 9 Jan · Shift 1 · Q64 · MCQ
A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30o from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s $-$ 1) will be (g = 10 ms $-$ … Includes diagram2019 · 9 Jan · Shift 2 · Q50 · MCQ
A particle of mass m is moving along a trajectory given by x = x0 + a cos $ω$ 1t y = y0 + b sin $ω$ 2t The torque, acting on the particle about the origin, at t = 0 is :2019 · 10 Apr · Shift 1 · Q53 · MCQ
Two coaxial discs, having moments of inertia I1 and I1/2, are rotating with respective angular velocities $ω$ 1 and $ω$ 1/2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a…2019 · 10 Apr · Shift 1 · Q55 · MCQ
A thin disc of mass M and radius R has mass per unit area $σ$ (r) = kr2 where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :2019 · 10 Apr · Shift 1 · Q56 · MCQ
The time dependence of the position of a particle of mass m = 2 is given by $r (t) = 2 t i - 3 t^{2} j$ . Its angular momentum, with respect to the origin, at time t = 2 is2019 · 10 Apr · Shift 2 · Q46 · MCQ
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $\frac{7 M}{8}$ and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I1 be…2019 · 10 Apr · Shift 2 · Q50 · MCQ
A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in… Includes diagram2019 · 10 Apr · Shift 2 · Q61 · MCQ
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -2019 · 10 Jan · Shift 1 · Q50 · MCQ
To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if…2019 · 10 Jan · Shift 1 · Q60 · MCQ
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is : Includes diagram2019 · 10 Jan · Shift 2 · Q47 · MCQ
A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular… Includes diagram2019 · 10 Jan · Shift 2 · Q54 · MCQ
An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G… Includes diagram2019 · 11 Jan · Shift 1 · Q48 · MCQ
A slab is subjected to two forces $F_{1}$ and $F_{2}$ of same magnitude F as shown in the figure. Force $F_{2}$ is in XY-plane while force $F_{1}$ acts along z = axis… Includes diagram2019 · 11 Jan · Shift 1 · Q49 · MCQ
A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular… Includes diagram2019 · 11 Jan · Shift 2 · Q43 · MCQ
A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO' ,passing through the… Includes diagram2019 · 11 Jan · Shift 2 · Q48 · MCQ
The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5m, the angle between the force and the position vector is (in radians) :2019 · 11 Jan · Shift 2 · Q51 · MCQ
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $θ$ 0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves…2019 · 12 Apr · Shift 1 · Q45 · MCQ
A uniform rod of length $ℓ$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis,…2019 · 12 Apr · Shift 1 · Q63 · MCQ
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $(\frac{σ _{0}}{r})$ , then the radius of gyration of the disc about its axis passing… Includes diagram2019 · 12 Apr · Shift 1 · Q67 · MCQ
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is :2019 · 12 Jan · Shift 1 · Q60 · MCQ
Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed $ω$ . At t = 0, their positions and direction of motion are shown in the figure. : The relative velocity $V_{A} - V_{B}$ … Includes diagram2019 · 12 Jan · Shift 2 · Q48 · MCQ
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly ?2019 · 12 Jan · Shift 2 · Q58 · MCQ
A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. when the particle… Includes diagram2019 · 12 Jan · Shift 2 · Q66 · MCQ
A force of $40 N$ acts on a point $B$ at the end of an $L$ -shaped object, as shown in the figure. The angle $θ$ that will produce maximum moment of the force about point $A$ is given by : Includes diagram2018 · 15 Apr · Shift 1 · Q51 · MCQ
A uniform rod $A B$ is suspended from a point $X,$ at a variable distance $x$ from $A$ , as shown, To make the rod horizontal, a mass $m$ is suspended from its end $A .$ A $se t o f$ (m,x)$$ values is recorded. The appropriate variables that… Includes diagram2018 · 15 Apr · Shift 1 · Q70 · MCQ
A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $α$ with the horizontal, will be proportional to : (see figure) Includes diagram2018 · 15 Apr · Shift 2 · Q54 · MCQ
A thin uniform bar of length $L$ and mass $8$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2 $υ$ and $υ$ respectively. The… Includes diagram2018 · 15 Apr · Shift 2 · Q55 · MCQ
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be : Includes diagram2018 · 16 Apr · Shift 1 · Q72 · MCQ
From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre… Includes diagram2018 · Shift 0 · Q60 · MCQ
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is : Includes diagram2018 · Shift 0 · Q63 · MCQ
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the… Includes diagram2017 · 8 Apr · Shift 1 · Q55 · MCQ
In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?2017 · 8 Apr · Shift 1 · Q56 · MCQ