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Rotational Motion

59 questions · Physics · JEE Advanced

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JEE Advanced
Physics
Rotational Motion

Rotational Motion

59 questions · Physics · JEE Advanced

The center of a disk of radius $r$ and mass $m$ is attached to a spring of spring constant $k$ , inside a ring of radius $R > r$ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring… Includes diagram2025 · Shift 1 · Q33 · MCQ
A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass $M$ and… Includes diagram2024 · Shift 1 · Q43 · Numerical
A thin uniform rod of length $L$ and certain mass is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$ … Includes diagram2024 · Shift 1 · Q47 · Numerical
A bar of mass $M = 1.00 kg$ and length $L = 0.20 m$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m = 0.10 kg$ is moving on…2023 · Shift 1 · Q38 · MCQ
Two point-like objects of masses $30 gm$ and $10 cm$ are fixed at the two ends of a rigid massless rod of length $10 cm$ . This system is suspended vertically from a rigid ceiling using a thin wire attached to… Includes diagram2023 · Shift 1 · Q47 · Numerical
An annular disk of mass $M$ , inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $μ$ , as shown in the figure. At some time, an impulse $J_{0} \overset{x}{^}$ is applied at a height $h$ above the… Includes diagram2023 · Shift 2 · Q40 · Multiple correct
A thin circular coin of mass $5 gm$ and radius $x y$ is initially in a horizontal $x y$ -plane. The coin is tossed vertically up ( $+ z$ direction) by applying an impulse of $\frac{π}{2} \times 1 0^{- 2} N$ … Includes diagram2023 · Shift 2 · Q42 · Numerical
At time $t = 0$ , a disk of radius $α = \frac{2}{3} rad s^{- 2}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $α = \frac{2}{3} rad s^{- 2}$ . A small stone is stuck to the disk. At $t = 0$ , it is…2022 · Shift 1 · Q41 · Numerical
A solid sphere of mass $1 m$ and radius $θ = 3 0^{\circ}$ rolls without slipping on a fixed inclined plane with an angle of inclination $θ = 3 0^{\circ}$ from the horizontal. Two forces of magnitude $1 N$ each,… Includes diagram2022 · Shift 1 · Q42 · Numerical
List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in $m s^{- 1}$ ) at time $t = \frac{π}{3} s$ . Which one of the… Includes table Includes diagram2022 · Shift 1 · Q52 · MCQ
A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$ , as shown in the figure. A… Includes diagram2022 · Shift 2 · Q51 · MCQ
A horizontal force F is applied at the center of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $μ$ . The center of… Includes diagram2021 · Shift 1 · Q49 · Multiple correct
A thin rod of mass M and length a is free to rotate in horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its center at a distance a/4 from the… Includes diagram2021 · Shift 1 · Q56 · Numerical
A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure… Includes diagram2020 · Shift 1 · Q37 · MCQ
A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now… Includes diagram2020 · Shift 2 · Q45 · Multiple correct
A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following…2019 · Shift 2 · Q41 · Multiple correct
Two vectors $A$ and $B$ are defined as $A = a i$ and $B = a$ $(cos ω T i + sin ω t j),$ where $a$ is a constant and $ω = π /6 r a d s^{- 1} .$ …2018 · Shift 1 · Q37 · Numerical
Consider a body of mass $1.0 k g$ at rest at the origin at time $t = 0.$ A force $F = (α t i + β j)$ is applied on the body, where $α = 1.0 N s^{- 1}$ and $β = 1.0 N .$ The…2018 · Shift 1 · Q38 · Multiple correct
A ring and disc are initially at rest, side by side, at the top of an inclined plane which makes an angle $6 0^{\circ}$ with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the…2018 · Shift 1 · Q42 · Numerical
The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V (r) = k r^{2} /2,$ where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit…2018 · Shift 1 · Q54 · Multiple correct
A block of mass $M$ has a circular cut with a frictionless surface as shown. The block resets on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x = 0,$ in a co-ordinate system fixed to the… Includes diagram2017 · Shift 1 · Q54 · Multiple correct
Consider regular polygons with number of sides $n = 3, 4, 5....$ as shown in the figure. The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and… Includes diagram2017 · Shift 2 · Q44 · MCQ
A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the… Includes diagram2017 · Shift 2 · Q48 · Multiple correct
A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $θ$ . Which of the following statements… Includes diagram2017 · Shift 2 · Q49 · Multiple correct
One twirls a circular ring (of mass M and radius R) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the… Includes diagram2017 · Shift 2 · Q53 · MCQ
One twirls a circular ring (of mass M and radius R) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the… Includes diagram2017 · Shift 2 · Q54 · MCQ
The position vector $r$ of a particle of mass m is given by the following equation $r (t) = α t^{3} i + β t^{2} j,$ where $α = \frac{10}{3} m s^{- 3}$ , $β = 5 m s^{- 2}$ …2016 · Shift 1 · Q40 · Multiple correct
A uniform wooden stick of mass 1.6 kg and length $l$ rests in an inclined manner on a smooth, vertical wall of height h ( < $l$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick…2016 · Shift 1 · Q41 · MCQ
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, rigid rod of length $l = 24 a$ through their centers. This assembly is laid on a firm and flat surface, and set… Includes diagram2016 · Shift 2 · Q40 · Multiple correct
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular… Includes diagram2016 · Shift 2 · Q51 · MCQ
A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular… Includes diagram2016 · Shift 2 · Q52 · MCQ
Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds v1 and v2, respectively, and always remain in contact with the surfaces. If they reach B and D with… Includes diagram2015 · Shift 1 · Q51 · Numerical
A ring of mass M and radius R is rotating with angular speed $ω$ about a fixed vertical axis passing through its centre O with two point masses each of mass $\frac{M}{8}$ at rest at O. These masses can move radially outwards along two… Includes diagram2015 · Shift 1 · Q53 · Multiple correct
The densities of two solid spheres A and B of the same radii R vary with radial distance r as $ρ_{A} (r) = k (\frac{r}{R})$ and $ρ_{B} (r) = k (\frac{r}{R})^{5}$ , , respectively, where k is a constant.…2015 · Shift 2 · Q43 · Numerical
A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ… Includes diagram2014 · Shift 1 · Q56 · Numerical
A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on… Includes diagram2014 · Shift 1 · Q59 · Numerical
A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed…2013 · Shift 1 · Q41 · Numerical
A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the xy-plane with centre at O and constant angular speed $ω$ . If the angular momentum of… Includes diagram2012 · Shift 1 · Q46 · MCQ
A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $ω$ , as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the rod… Includes diagram2012 · Shift 1 · Q48 · MCQ
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $ω$ . The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as… Includes diagram2012 · Shift 2 · Q41 · MCQ
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $ω$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $\frac{ω}{2}$ … Includes diagram2012 · Shift 2 · Q48 · Multiple correct
Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass…2012 · Shift 2 · Q49 · Multiple correct
Consider a disc rotating in the horizontal plane with a constant angular speed $ω$ about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the… Includes diagram2012 · Shift 2 · Q50 · MCQ
The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be… Includes diagram2012 · Shift 2 · Q53 · MCQ
The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be… Includes diagram2012 · Shift 2 · Q54 · MCQ
Four solid spheres each of diameter $5$ cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N $\times$ 10−4 kg-m2, then N is Includes diagram2011 · Shift 1 · Q51 · Numerical
A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R ( < L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached : (case A). The disc is not free to rotate… Includes diagram2011 · Shift 1 · Q60 · Multiple correct
A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.2 m/s2. The coefficient of friction between the… Includes diagram2011 · Shift 1 · Q66 · Numerical
If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that2009 · Shift 1 · Q52 · Multiple correct
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then, Includes diagram2009 · Shift 2 · Q46 · Multiple correct
STATEMENT - 1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder…2008 · Shift 1 · Q59 · MCQ
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically… Includes diagram2008 · Shift 2 · Q61 · MCQ
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically… Includes diagram2008 · Shift 2 · Q62 · MCQ
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically… Includes diagram2008 · Shift 2 · Q63 · MCQ
Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moment of inertia $I$ and $2 I$ respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 ω$ using the entire potential…2007 · Shift 1 · Q56 · MCQ
Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moment of inertia $I$ and $2 I$ respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 ω$ using the entire potential…2007 · Shift 1 · Q57 · MCQ
Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moment of inertia $I$ and $2 I$ respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 ω$ using the entire potential…2007 · Shift 1 · Q58 · MCQ
A small object of uniform density rolls up a curved surface with an initial velocity $v$ . It reaches up to a maximum height of $\frac{3 v ^{2}}{4 g}$ with respect to the initial position. The object is Includes diagram2007 · Shift 2 · Q12 · MCQ
STATEMENT 1 If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant. Because STATEMENT 2 The linear momentum of an isolated system remains constant.2007 · Shift 2 · Q18 · MCQ