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Rotational Motion

86 questions · Physics · NEET

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Physics
Rotational Motion

Rotational Motion

86 questions · Physics · NEET

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of $6 0^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (Take $g = 10 m / s^{2}$ …2025 · Q151 · MCQ
The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.2025 · Q167 · MCQ
A sphere of radius $R$ is cut from a larger solid sphere of radius $2 R$ as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the $Y$ -axis is: Includes diagram2025 · Q171 · MCQ
A bob is whirled in a horizontal plane by means of a string with an initial speed of $T$ . The tension in the string is $T$ . If speed becomes $2 ω$ while keeping the same radius, the tension in the string becomes:2024 · Q162 · MCQ
The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $2400 g cm^{2}$ . The length of the $400 g$ rod is nearly:2024 · Q166 · MCQ
A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $v$ in the direction shown, which one of the following options is correct ( $P$ and $Q$ are any highest and lowest points on the… Includes diagram2024 · Q185 · MCQ
The radius of gyration of a solid sphere of mass $X Y$ about $X Y$ is $\frac{5 x}{7} m$ as shown in figure. The radius of the sphere is $\frac{5 x}{7} m$ , then the value of $x$ is: Includes diagram2024 · Q166 · MCQ
A constant torque of $100 N m$ turns a wheel of moment of inertia $300 kg m^{2}$ about an axis passing through its centre. Starting from rest, its angular velocity after $3 s$ is :-2023 · Q169 · MCQ
The ratio of radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-2023 · Q128 · MCQ
The angular acceleration of a body, moving along the circumference of a circle, is :2023 · Q155 · MCQ
An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :2022 · Q137 · MCQ
The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is2022 · Q128 · MCQ
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is2022 · Q144 · MCQ
From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90 $^{\circ}$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to the…2021 · Q161 · MCQ
A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find… Includes diagram2021 · Q171 · MCQ
Find the torque about the origin when a force of 3 $\hat{j}$ N acts on a particle whose position vector is 2 $\hat{k}$ m.2020 · Q149 · MCQ
A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?2019 · Q125 · MCQ
Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :2019 · Q126 · MCQ
A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 $π$ revolutions is :2019 · Q149 · MCQ
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is2018 · Q143 · MCQ
A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?2018 · Q144 · MCQ
Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $ω$ about their own symmetry axes. The amounts of work (W)…2018 · Q146 · MCQ
The moment of the force, $F = 4 i + 5 j - 6 k$ at (2, 0, –3), about the point (2, –2, –2), is given by2018 · Q149 · MCQ
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?2017 · Q151 · MCQ
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $ω_{1}$ and $ω_{2}$ . They are brought into contact face to face…2017 · Q152 · MCQ
A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?2016 · Q147 · MCQ
From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?2016 · Q148 · MCQ
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s $-$ 2.…2016 · Q149 · MCQ
Two rotating bodies A and B of masses m and 2m with moments of inertia $I_{A}$ and $I_{B}$ ( $I_{B}$ > $I_{A}$ ) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then2016 · Q147 · MCQ
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic…2016 · Q148 · MCQ
A light rod of length $l$ has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is2016 · Q149 · MCQ
A force $F = α i + 3 j + 6 k$ is acting at a point $r = 2 i - 6 j - 12 k$ . The value of $α$ for which angular momentum about origin is…2015 · Q128 · MCQ
An automobile moves on a road with a speed of 54 km h $-$ 1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average…2015 · Q137 · MCQ
Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass… Includes diagram2015 · Q138 · MCQ
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of… Includes diagram2015 · Q134 · MCQ
A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction…2015 · Q143 · MCQ
A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown. the tension in the string is increased gradually and… Includes diagram2015 · Q144 · MCQ
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an…2014 · Q146 · MCQ
The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $θ$ without slipping and slipping down the incline without rolling is2014 · Q147 · MCQ
The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are2013 · Q151 · MCQ
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s $-$ 1. Disc D2 has 4 kg mass, 0.1 m radius and initial…2013 · Q152 · MCQ
A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of $\frac{3 v ^{2}}{4 g}$ with respect to the initial position. The object is2013 · Q148 · MCQ
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is Includes diagram2013 · Q149 · MCQ
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through Includes diagram2012 · Q102 · MCQ
A car of mass m is moving on a level circular track of radius R. If $μ$ s represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by2012 · Q103 · MCQ
A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the…2012 · Q104 · MCQ
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along2012 · Q160 · MCQ
A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45o, the speed of the car is2012 · Q161 · MCQ
ABC is an equilateral triangle with O as its centre. $F_{1}, F_{2}$ and $F_{3}$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is… Includes diagram2012 · Q162 · MCQ
A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of… Includes diagram2011 · Q103 · MCQ
The instantaneous angular position of a point on a rotating wheel is given by the equation $θ (t) = 2 t^{3} - 6 t^{2}$ The torque on the wheel becomes zero at2011 · Q155 · MCQ
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $I$ 0. Its moment of inertia about an axis passing through one of its ends and perpendicular to…2011 · Q156 · MCQ
A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $ω$ . Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with…2010 · Q95 · MCQ
A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?2010 · Q96 · MCQ
From a circular disc of radius R and mass 9M, a small disc of mass M and radius $\frac{R}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through…2010 · Q97 · MCQ
A circular disk of moment of inertia $I_{t}$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $ω_{i}$ . Another disk of moment of inertia $I_{b}$ is dropped coaxially onto the rotating disk.…2010 · Q172 · MCQ
A gramophone record is revolving with an angular velocity $ω$ . A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $μ$ . The coin will revolve with the record if2010 · Q174 · MCQ
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $ω$ . If two objects each of mass m be attached gently to the opposite ends of a…2009 · Q161 · MCQ
Four identical thin rods each of mass M and length $l$ , form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is2009 · Q162 · MCQ
If $F$ is the force acting on a particle having position vector $r$ and $τ$ be the torque of this force about the origin, then2009 · Q163 · MCQ
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is2008 · Q145 · MCQ
A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined…2008 · Q156 · MCQ
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then Includes diagram2007 · Q136 · MCQ
A uniform rod AB of length $l$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod… Includes diagram2007 · Q137 · MCQ
A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of2007 · Q138 · MCQ
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $ω$ . The force exerted…2006 · Q151 · MCQ
A uniform rod AB of length $l$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod…2006 · Q161 · MCQ
The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc2006 · Q162 · MCQ
A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $θ$ . The frictional force2005 · Q161 · MCQ
The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is2005 · Q162 · MCQ
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio2005 · Q163 · MCQ
A round disc of moment of inertia $I$ 2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I$ 1 rotating with an angular velocity $ω$ about the same axis. The…2004 · Q139 · MCQ
Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side $l$ cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in… Includes diagram2004 · Q147 · MCQ
A wheel having moment of inertia 2 kg m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be2004 · Q148 · MCQ
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axes in the plane of the ring is2004 · Q151 · MCQ
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be2003 · Q159 · MCQ
A stone is tied to a string of length $l$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change…2003 · Q160 · MCQ
A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?2003 · Q161 · MCQ
A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $ω$ . Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular…2003 · Q162 · MCQ
A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (if radius of wheel is 1 m)2002 · Q158 · MCQ
A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct ?2002 · Q159 · MCQ
A disc is rotating with angular speed $ω$ . If a child sits on it, what is conserved2002 · Q160 · MCQ
A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with2002 · Q161 · MCQ
For the adjoining diagram, the correct relation between I1, I2, and I3 is, (I-moment of inertia) Includes diagram2000 · Q153 · MCQ
For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier2000 · Q154 · MCQ
As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break Includes diagram2000 · Q155 · MCQ