Rotational Motion · Physics · JEE Advanced

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MCQ (More than One Correct Answer)

JEE Advanced 2023 Paper 2 Online
An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $\mu$, as shown in t...
JEE Advanced 2021 Paper 1 Online
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...
JEE Advanced 2020 Paper 2 Offline
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 horizonta...
JEE Advanced 2019 Paper 2 Offline
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 rotat...
JEE Advanced 2018 Paper 1 Offline
The potential energy of a particle of mass $$m$$ at a distance $$r$$ from a fixed point $$O$$ is given by $$V\left( r \right) = k{r^2}/2,$$ where $$k$...
JEE Advanced 2018 Paper 1 Offline
Consider a body of mass $$1.0$$ $$kg$$ at rest at the origin at time $$t=0.$$ A force $$\overrightarrow F = \left( {\alpha t \widehat i + \beta \wide...
JEE Advanced 2017 Paper 2 Offline
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...
JEE Advanced 2017 Paper 2 Offline
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, t...
JEE Advanced 2017 Paper 1 Offline
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 tabl...
JEE Advanced 2016 Paper 2 Offline
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 $$l = \sqrt {24...
JEE Advanced 2016 Paper 1 Offline
The position vector $$\overrightarrow r $$ of a particle of mass m is given by the following equation $$$\overrightarrow r \left( t \right) = \alpha {...
JEE Advanced 2015 Paper 1 Offline
A ring of mass M and radius R is rotating with angular speed $$\omega$$ about a fixed vertical axis passing through its centre O with two point masses...
IIT-JEE 2012 Paper 2 Offline
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 h...
IIT-JEE 2012 Paper 2 Offline
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 $$...
IIT-JEE 2011 Paper 1 Offline
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 th...
IIT-JEE 2009 Paper 2 Offline
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 spher...
IIT-JEE 2009 Paper 1 Offline
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 that

Numerical

JEE Advanced 2023 Paper 2 Online
A thin circular coin of mass $5 \mathrm{gm}$ and radius $4 / 3 \mathrm{~cm}$ is initially in a horizontal $x y$-plane. The coin is tossed vertically u...
JEE Advanced 2023 Paper 1 Online
Two point-like objects of masses $20 ~\mathrm{gm}$ and $30 ~\mathrm{gm}$ are fixed at the two ends of a rigid massless rod of length $10 \mathrm{~cm}$...
JEE Advanced 2022 Paper 1 Online
At time $t=0$, a disk of radius $1 \mathrm{~m}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}...
JEE Advanced 2022 Paper 1 Online
A solid sphere of mass $1 \mathrm{~kg}$ and radius $1 \mathrm{~m}$ rolls without slipping on a fixed inclined plane with an angle of inclination $\the...
JEE Advanced 2021 Paper 1 Online
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 m...
JEE Advanced 2018 Paper 1 Offline
Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are defined as $$\overrightarrow A $$ $$=$$ $$a\widehat i$$ and $$\overrightarrow B = ...
JEE Advanced 2018 Paper 1 Offline
A ring and disc are initially at rest, side by side, at the top of an inclined plane which makes an angle $${60^ \circ }$$ with the horizontal. They ...
JEE Advanced 2015 Paper 2 Offline
The densities of two solid spheres A and B of the same radii R vary with radial distance r as $${\rho _A}(r) = k\left( {{r \over R}} \right)$$ and $${...
JEE Advanced 2015 Paper 1 Offline
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, r...
JEE Advanced 2014 Paper 1 Offline
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 =...
JEE Advanced 2014 Paper 1 Offline
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...
JEE Advanced 2013 Paper 1 Offline
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 u...
IIT-JEE 2011 Paper 1 Offline
Four solid spheres each of diameter $$\sqrt 5 $$ cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment ...
IIT-JEE 2011 Paper 1 Offline
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 w...

MCQ (Single Correct Answer)

JEE Advanced 2023 Paper 1 Online
A bar of mass $M=1.00 \mathrm{~kg}$ and length $L=0.20 \mathrm{~m}$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a ...
JEE Advanced 2022 Paper 2 Online
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 ra...
JEE Advanced 2022 Paper 1 Online
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 ...
JEE Advanced 2020 Paper 1 Offline
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 positi...
JEE Advanced 2017 Paper 2 Offline
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 ...
JEE Advanced 2017 Paper 2 Offline
The total kinetic energy of the ring is
JEE Advanced 2017 Paper 2 Offline
The minimum value of $$\omega$$0 below which the ring will drop down is
JEE Advanced 2016 Paper 2 Offline
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 ...
JEE Advanced 2016 Paper 2 Offline
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 ...
JEE Advanced 2016 Paper 1 Offline
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 s...
IIT-JEE 2012 Paper 2 Offline
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega $$. The discs ...
IIT-JEE 2012 Paper 2 Offline
Consider a disc rotating in the horizontal plane with a constant angular speed $$\omega $$ about its centre O. The disc has a shaded region on one sid...
IIT-JEE 2012 Paper 2 Offline
Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?
IIT-JEE 2012 Paper 2 Offline
Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?
IIT-JEE 2012 Paper 1 Offline
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...
IIT-JEE 2012 Paper 1 Offline
A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $$\omega$$, as shown in the figure. At time t = 0, a...
IIT-JEE 2008 Paper 2 Offline
The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is :
IIT-JEE 2008 Paper 2 Offline
The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to:
IIT-JEE 2008 Paper 2 Offline
The maximum value of V$$_0$$ for which the disk will roll without slipping is:
IIT-JEE 2008 Paper 1 Offline
STATEMENT - 1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to...
IIT-JEE 2007 Paper 2 Offline
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}...
IIT-JEE 2007 Paper 2 Offline
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 STATE...
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