# Rotational Motion · Physics · JEE Main

Start Practice## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 5th April Morning Shift

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 s...

JEE Main 2024 (Online) 8th April Evening Shift

A thin circular disc of mass $$\mathrm{M}$$ and radius $$\mathrm{R}$$ is rotating in a horizontal plane about an axis passing through its centre and p...

JEE Main 2024 (Online) 1st February Evening Shift

A disc of radius $\mathrm{R}$ and mass $\mathrm{M}$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surfa...

JEE Main 2024 (Online) 30th January Morning Shift

A particle of mass $$\mathrm{m}$$ is projected with a velocity '$$\mathrm{u}$$' making an angle of $$30^{\circ}$$ with the horizontal. The magnitude o...

JEE Main 2024 (Online) 27th January Evening Shift

A heavy iron bar of weight $$12 \mathrm{~kg}$$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $$60...

JEE Main 2023 (Online) 13th April Morning Shift

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 $$\mathrm{A}$$ as show...

JEE Main 2023 (Online) 10th April Evening Shift

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$
Assertion A : An electr...

JEE Main 2022 (Online) 29th July Evening Shift

The torque of a force $$5 \hat{i}+3 \hat{j}-7 \hat{k}$$ about the origin is $$\tau$$. If the force acts on a particle whose position vector is $$2 i+2...

JEE Main 2022 (Online) 25th July Morning Shift

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 ...

JEE Main 2022 (Online) 29th June Morning Shift

A spherical shell of 1 kg mass and radius R is rolling with angular speed $$\omega$$ on horizontal plane (as shown in figure). The magnitude of angula...

JEE Main 2022 (Online) 28th June Evening Shift

A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 2t where t is in second and $$\alpha$$ is in rads$$-$$2. At t = 0, the ball has angula...

JEE Main 2022 (Online) 28th June Evening Shift

A $$\sqrt {34} $$ 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....

JEE Main 2022 (Online) 28th June Morning Shift

Match List-I with List-II
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JEE Main 2022 (Online) 27th June Evening Shift

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...

JEE Main 2022 (Online) 26th June Evening Shift

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...

JEE Main 2022 (Online) 26th June Morning Shift

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 ...

JEE Main 2022 (Online) 25th June Morning Shift

If force $$\overrightarrow F = 3\widehat i + 4\widehat j - 2\widehat k$$ acts on a particle position vector $$2\widehat i + \widehat j + 2\widehat k$...

JEE Main 2021 (Online) 31st August Evening Shift

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 s...

JEE Main 2021 (Online) 31st August Morning Shift

Angular momentum of a single particle moving with constant speed along circular path :

JEE Main 2021 (Online) 27th August Evening Shift

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 w...

JEE Main 2021 (Online) 27th August Morning Shift

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...

JEE Main 2021 (Online) 26th August Evening Shift

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 cylind...

JEE Main 2021 (Online) 27th July Morning Shift

List-I
List-II
(a) MI of the rod (length L, Mass M, about an axis $$ \bot $$ to the rod passing through the midpoint)
(i)...

JEE Main 2021 (Online) 27th July Morning Shift

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 arou...

JEE Main 2021 (Online) 25th July Morning Shift

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 d...

JEE Main 2021 (Online) 22th July Evening Shift

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 star...

JEE Main 2021 (Online) 20th July Evening Shift

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :

JEE Main 2021 (Online) 18th March Evening Shift

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 wir...

JEE Main 2021 (Online) 18th March Evening Shift

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 frictiona...

JEE Main 2021 (Online) 18th March Morning Shift

A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $$\omega$$. Two particles having mass m each are now atta...

JEE Main 2021 (Online) 17th March Evening Shift

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 ...

JEE Main 2021 (Online) 17th March Morning Shift

A triangular plate is shown. A force $$\overrightarrow F $$ = 4$$\widehat i$$ $$-$$ 3$$\widehat j$$ is applied at point P. The torque at point P with ...

JEE Main 2021 (Online) 17th March Morning Shift

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 c...

JEE Main 2021 (Online) 26th February Evening Shift

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...

JEE Main 2021 (Online) 26th February Morning Shift

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 ...

JEE Main 2021 (Online) 25th February Evening Shift

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $$\theta$$ and cli...

JEE Main 2021 (Online) 24th February Morning Shift

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. o...

JEE Main 2020 (Online) 6th September Evening Slot

The linear mass density of a thin rod AB of length L varies from A to B as
$$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$$...

JEE Main 2020 (Online) 6th September Morning Slot

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 $$\omega $$, abou...

JEE Main 2020 (Online) 6th September Morning Slot

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 inerti...

JEE Main 2020 (Online) 5th September Evening Slot

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...

JEE Main 2020 (Online) 5th September Morning Slot

A wheel is rotating freely with an angular speed
$$\omega $$ on a shaft. The moment of inertia of the
wheel is I and the moment of inertia of the
shaf...

JEE Main 2020 (Online) 4th September Evening Slot

Consider two uniform discs of the same thickness and different radii R1
= R and R2
= $$\alpha $$R made of
the same material. If the ratio of their m...

JEE Main 2020 (Online) 4th September Evening Slot

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 (...

JEE Main 2020 (Online) 3rd September Evening Slot

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 $$\ome...

JEE Main 2020 (Online) 3rd September Morning Slot

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 cylinde...

JEE Main 2020 (Online) 2nd September Evening Slot

Two uniform circular discs are rotating
independently in the same direction around
their common axis passing through their
centres. The moment of iner...

JEE Main 2020 (Online) 2nd September Morning Slot

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
ceilin...

JEE Main 2020 (Online) 2nd September Morning Slot

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 ...

JEE Main 2020 (Online) 9th January Evening Slot

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 ...

JEE Main 2020 (Online) 9th January Morning Slot

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 ...

JEE Main 2020 (Online) 8th January Evening Slot

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...

JEE Main 2020 (Online) 8th January Morning Slot

Consider a uniform rod of mass M = 4m and
length $$\ell $$ pivoted about its centre. A mass m
moving with velocity v making angle $$\theta = {\pi \o...

JEE Main 2020 (Online) 7th January Evening Slot

Mass per unit area of a circular disc of radius $$a$$ depends on the distance r from its centre as $$\sigma \left( r \right)$$ = A + Br
. The moment o...

JEE Main 2020 (Online) 7th January Morning Slot

The radius of gyration of a uniform rod of length $$l$$, about an axis passing through a
point $${l \over 4}$$ away from the centre of the rod,
and pe...

JEE Main 2020 (Online) 7th January Morning Slot

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. W...

JEE Main 2019 (Online) 12th April Morning Slot

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 $$\left( {{{{\sigma _0}...

JEE Main 2019 (Online) 12th April Morning Slot

A uniform rod of length $$\ell $$ is being rotated in a horizontal plane with a constant angular speed about an axis
passing through one of its ends. ...

JEE Main 2019 (Online) 12th April Morning Slot

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta $$0. If the
person stands up when the swing pass...

JEE Main 2019 (Online) 10th April Evening Slot

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 c...

JEE Main 2019 (Online) 10th April Evening Slot

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $${{7M} \over 8}$$
and is converted into a unifo...

JEE Main 2019 (Online) 10th April Evening Slot

The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$
....

JEE Main 2019 (Online) 10th April Morning Slot

A thin disc of mass M and radius R has mass
per unit area $$\sigma $$(r) = kr2 where r is the distance
from its centre. Its moment of inertia about an...

JEE Main 2019 (Online) 10th April Morning Slot

Two coaxial discs, having moments of inertia
I1 and I1/2, are rotating with respective angular
velocities $$\omega $$1 and
$$\omega $$1/2
, about the...

JEE Main 2019 (Online) 10th April Morning Slot

A particle of mass m is moving along a
trajectory given by
x = x0 + a cos$$\omega $$1t
y = y0 + b sin$$\omega $$2t
The torque, acting on the particle ...

JEE Main 2019 (Online) 9th April Evening Slot

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,...

JEE Main 2019 (Online) 9th April Evening Slot

A thin smooth rod of length L and mass M is
rotating freely with angular speed $$\omega $$0 about an
axis perpendicular to the rod and passing
through...

JEE Main 2019 (Online) 9th April Morning Slot

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 cy...

JEE Main 2019 (Online) 9th April Morning Slot

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 $$\theta $$, where ...

JEE Main 2019 (Online) 8th April Evening Slot

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 fie...

JEE Main 2019 (Online) 8th April Evening Slot

A solid sphere and solid cylinder of identical
radii approach an incline with the same linear
velocity (see figure). Both roll without slipping
all th...

JEE Main 2019 (Online) 8th April Evening Slot

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 of...

JEE Main 2019 (Online) 8th April Morning Slot

A thin circular plate of mass M and radius R
has its density varying as $$\rho $$(r) = $$\rho $$0r with $$\rho $$0 as
constant and r is the distance f...

JEE Main 2019 (Online) 12th January Evening Slot

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 ...

JEE Main 2019 (Online) 12th January Evening Slot

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 rep...

JEE Main 2019 (Online) 12th January Evening Slot

Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed $$\omega $$. At t = 0, their positions and directi...

JEE Main 2019 (Online) 12th January Morning Slot

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 ...

JEE Main 2019 (Online) 11th January Evening Slot

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...

JEE Main 2019 (Online) 11th January Evening Slot

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...

JEE Main 2019 (Online) 11th January Evening Slot

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...

JEE Main 2019 (Online) 11th January Morning Slot

A slab is subjected to two forces $$\overrightarrow {{F_1}} $$ and $$\overrightarrow {{F_2}} $$ of same magnitude F as shown in the figure. Force $$\...

JEE Main 2019 (Online) 11th January Morning Slot

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 cent...

JEE Main 2019 (Online) 10th January Evening Slot

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 (se...

JEE Main 2019 (Online) 10th January Evening Slot

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 o...

JEE Main 2019 (Online) 10th January Morning Slot

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 angula...

JEE Main 2019 (Online) 10th January Morning Slot

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, a...

JEE Main 2019 (Online) 9th January Evening Slot

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...

JEE Main 2019 (Online) 9th January Morning Slot

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 wit...

JEE Main 2019 (Online) 9th January Morning Slot

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 :

JEE Main 2018 (Online) 16th April Morning Slot

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 :
...

JEE Main 2018 (Offline)

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 t...

JEE Main 2018 (Offline)

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 remai...

JEE Main 2018 (Online) 15th April Evening Slot

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 pl...

JEE Main 2018 (Online) 15th April Evening Slot

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 t...

JEE Main 2018 (Online) 15th April Morning Slot

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 $$\theta $$ that will produce ma...

JEE Main 2018 (Online) 15th April Morning Slot

A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is s...

JEE Main 2017 (Online) 9th April Morning Slot

The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and t...

JEE Main 2017 (Online) 9th April Morning Slot

A circular hole of radius $${R \over 4}$$ is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the...

JEE Main 2017 (Online) 8th April Morning Slot

Moment of inertia of an equilateral triangular lamina ABC, about the axis
passing through its centre O and perpendicular to its plane is Io as shown ...

JEE Main 2017 (Online) 8th April Morning Slot

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 pan...

JEE Main 2017 (Online) 8th April Morning Slot

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...

JEE Main 2017 (Offline)

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$.
What is the ratio $${l \over R}$$ ...

JEE Main 2017 (Offline)

A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it
can rotate in a vertical plane (see figure). There is negligible fri...

JEE Main 2016 (Online) 10th April Morning Slot

Concrete mixture is made by mixing cement, stone and sand in a rotating
cylindrical drum. If the drum rotates too fast, the ingredients remain stuck t...

JEE Main 2016 (Online) 9th April Morning Slot

A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. T...

JEE Main 2016 (Offline)

A roller is made by joining together two cones at their vertices $$0$$. It is kept on two rails $$AB$$ and $$CD$$, which are placed asymmetrically (se...

JEE Main 2015 (Offline)

From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through i...

JEE Main 2014 (Offline)

A bob of mass $$m$$ attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rotates in a horizontal circle wi...

JEE Main 2014 (Offline)

A mass $$'m'$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$ If the string does not slip o...

JEE Main 2013 (Offline)

A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal surface. The initial velocity ...

AIEEE 2011

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc...

AIEEE 2011

A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$$ and radius $$R.$$ Assuming p...

AIEEE 2011

A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where $$t$$ is measured in seconds) ...

AIEEE 2010

A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}$$ in the $$x$$-$$y$$ plane as...

AIEEE 2009

A thin uniform rod of length $$l$$ and mass $$m$$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\...

AIEEE 2008

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and p...

AIEEE 2007

A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rolls down (without slipping) an inclined plane making an angle $$\theta ...

AIEEE 2007

Angular momentum of the particle rotating with a central force is constant due to

AIEEE 2007

For the given uniform square lamina $$ABCD$$, whose center is $$O,$$
...

AIEEE 2006

A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega $$. Two objects each of mass ...

AIEEE 2006

Four point masses, each of value $$m,$$ are placed at the corners of a square $$ABCD$$ of side $$l$$. The moment of inertia of this system about an ax...

AIEEE 2006

A force of $$ - F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$$ is
...

AIEEE 2005

An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular speed. The ratio of the forces e...

AIEEE 2005

The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the plane of the disc through the ce...

AIEEE 2004

One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia about their diameters are respec...

AIEEE 2004

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the following will not be affected ?

AIEEE 2003

A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is

AIEEE 2003

Let $$\overrightarrow F $$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\overrightarrow \tau $$ be the tor...

AIEEE 2003

A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $$4$$ $$R$$ is made from an iro...

AIEEE 2002

Initial angular velocity of a circular disc of mass $$M$$ is $${\omega _1}.$$ Then two small spheres of mass $$m$$ are attached gently to diametricall...

AIEEE 2002

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum a...

AIEEE 2002

A particle of mass $$m$$ moves along line PC with velocity $$v$$ as shown. What is the angular momentum of the particle about P?
...

AIEEE 2002

Moment of inertia of a circular wire of mass $$M$$ and radius $$R$$ about its diameter is

## Numerical

JEE Main 2024 (Online) 9th April Evening Shift

A circular disc reaches from top to bottom of an inclined plane of length $$l$$. When it slips down the plane, if takes $$t \mathrm{~s}$$. When it rol...

JEE Main 2024 (Online) 9th April Morning Shift

A string is wrapped around the rim of a wheel of moment of inertia $$0.40 \mathrm{~kgm}^2$$ and radius $$10 \mathrm{~cm}$$. The wheel is free to rotat...

JEE Main 2024 (Online) 8th April Evening Shift

A circular table is rotating with an angular velocity of $$\omega \mathrm{~rad} / \mathrm{s}$$ about its axis (see figure). There is a smooth groove a...

JEE Main 2024 (Online) 4th April Morning Shift

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 reache...

JEE Main 2024 (Online) 1st February Evening Shift

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2 \mathrm{~Ns...

JEE Main 2024 (Online) 31st January Evening Shift

A body of mass '$$m$$' is projected with a speed '$$u$$' making an angle of $$45^{\circ}$$ with the ground. The angular momentum of the body about the...

JEE Main 2024 (Online) 31st January Evening Shift

Two identical spheres each of mass $$2 \mathrm{~kg}$$ and radius $$50 \mathrm{~cm}$$ are fixed at the ends of a light rod so that the separation betwe...

JEE Main 2024 (Online) 30th January Evening Shift

Two discs of moment of inertia $$I_1=4 \mathrm{~kg} \mathrm{~m}^2$$ and $$I_2=2 \mathrm{~kg} \mathrm{~m}^2$$, about their central axes & normal to the...

JEE Main 2024 (Online) 30th January Morning Shift

Consider a Disc of mass $$5 \mathrm{~kg}$$, radius $$2 \mathrm{~m}$$, rotating with angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ about an ax...

JEE Main 2024 (Online) 29th January Evening Shift

A body of mass $$5 \mathrm{~kg}$$ moving with a uniform speed $$3 \sqrt{2} \mathrm{~ms}^{-1}$$ in $$X-Y$$ plane along the line $$y=x+4$$. The angular ...

JEE Main 2024 (Online) 29th January Morning Shift

A cylinder is rolling down on an inclined plane of inclination $$60^{\circ}$$. It's acceleration during rolling down will be $$\frac{x}{\sqrt{3}} m / ...

JEE Main 2024 (Online) 27th January Evening Shift

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 rat...

JEE Main 2024 (Online) 27th January Morning Shift

Four particles each of mass $$1 \mathrm{~kg}$$ are placed at four corners of a square of side $$2 \mathrm{~m}$$. Moment of inertia of system about an ...

JEE Main 2023 (Online) 15th April Morning Shift

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 gyratio...

JEE Main 2023 (Online) 13th April Evening Shift

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 t...

JEE Main 2023 (Online) 13th April Morning Shift

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 e...

JEE Main 2023 (Online) 12th April Morning Shift

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $$\frac{x}{5}$$. The value of $$x$$ is ___________....

JEE Main 2023 (Online) 11th April Evening Shift

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $$...

JEE Main 2023 (Online) 11th April Morning Shift

A solid sphere of mass $$500 \mathrm{~g}$$ and radius $$5 \mathrm{~cm}$$ is rotated about one of its diameter with angular speed of $$10 ~\mathrm{rad}...

JEE Main 2023 (Online) 10th April Evening Shift

A force of $$-\mathrm{P} \hat{\mathrm{k}}$$ acts on the origin of the coordinate system. The torque about the point $$(2,-3)$$ is $$\mathrm{P}(a \hat{...

JEE Main 2023 (Online) 8th April Evening Shift

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $$3 \mathrm{~m} / \mathrm{s}$$ (as shown in figure). Max...

JEE Main 2023 (Online) 8th April Morning Shift

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} \mathr...

JEE Main 2023 (Online) 6th April Evening Shift

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 p...

JEE Main 2023 (Online) 6th April Morning Shift

Two identical solid spheres each of mass $$2 \mathrm{~kg}$$ and radii $$10 \mathrm{~cm}$$ are fixed at the ends of a light rod. The separation between...

JEE Main 2023 (Online) 1st February Evening Shift

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 ...

JEE Main 2023 (Online) 1st February Morning Shift

A solid cylinder is released from rest from the top of an inclined plane of inclination $$30^{\circ}$$ and length $$60 \mathrm{~cm}$$. If the cylinder...

JEE Main 2023 (Online) 31st January Evening Shift

Two discs of same mass and different radii are made of different materials such that their
thicknesses are $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$ re...

JEE Main 2023 (Online) 31st January Morning Shift

A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10^{-3} \mathrm{~J}$$. The speed...

JEE Main 2023 (Online) 30th January Evening Shift

A uniform disc of mass $0.5 \mathrm{~kg}$ and radius $r$ is projected with velocity $18 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=0$ s on a rough horiz...

JEE Main 2023 (Online) 30th January Morning Shift

A thin uniform rod of length $$2 \mathrm{~m}$$, cross sectional area '$$A$$' and density '$$\mathrm{d}$$' is rotated about an axis passing through the...

JEE Main 2023 (Online) 29th January Evening Shift

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...

JEE Main 2023 (Online) 29th January Morning Shift

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 wi...

JEE Main 2023 (Online) 25th January Evening Shift

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 pl...

JEE Main 2023 (Online) 25th January Morning Shift

$$\mathrm{I_{CM}}$$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. ...

JEE Main 2023 (Online) 24th January Evening Shift

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 radi...

JEE Main 2023 (Online) 24th January Morning Shift

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 $$\sqrt x$$ cm. The valu...

JEE Main 2022 (Online) 28th July Morning Shift

Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of in...

JEE Main 2022 (Online) 27th July Evening Shift

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, ...

JEE Main 2022 (Online) 27th July Morning Shift

A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\right) N$$ applied tangentially (...

JEE Main 2022 (Online) 26th July Evening Shift

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ___________ $...

JEE Main 2022 (Online) 26th July Morning Shift

A disc of mass $$1 \mathrm{~kg}$$ and radius $$\mathrm{R}$$ is free to rotate about a horizontal axis passing through its centre and perpendicular to ...

JEE Main 2022 (Online) 30th June Morning Shift

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 ...

JEE Main 2022 (Online) 29th June Evening Shift

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 ...

JEE Main 2022 (Online) 28th June Evening Shift

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...

JEE Main 2022 (Online) 28th June Morning Shift

The position vector of 1 kg object is $$\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$$ and its velocity $$\overrightarrow v = \lef...

JEE Main 2022 (Online) 27th June Evening Shift

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...

JEE Main 2022 (Online) 25th June Evening Shift

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...

JEE Main 2022 (Online) 24th June Morning Shift

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...

JEE Main 2021 (Online) 1st September Evening Shift

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...

JEE Main 2021 (Online) 26th August Morning Shift

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...

JEE Main 2021 (Online) 27th July Evening Shift

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 ene...

JEE Main 2021 (Online) 25th July Evening Shift

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 th...

JEE Main 2021 (Online) 25th July Morning Shift

A particle of mass 'm' is moving in time 't' on a trajectory given by$$\overrightarrow r = 10\alpha {t^2}\widehat i + 5\beta (t - 5)\widehat j$$Where...

JEE Main 2021 (Online) 22th July Evening Shift

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 mov...

JEE Main 2021 (Online) 20th July Evening Shift

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 ra...

JEE Main 2021 (Online) 20th July Evening Shift

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 ______...

JEE Main 2021 (Online) 20th July Morning Shift

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 th...

JEE Main 2021 (Online) 17th March Morning Shift

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 i...

JEE Main 2021 (Online) 17th March Morning Shift

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 slipp...

JEE Main 2021 (Online) 16th March Evening Shift

A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The accelerat...

JEE Main 2021 (Online) 16th March Evening Shift

A force $$\overrightarrow F $$ = $${4\widehat i + 3\widehat j + 4\widehat k}$$ is applied on an intersection point of x = 2 plane and x-axis. The magn...

JEE Main 2021 (Online) 16th March Morning Shift

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 consta...

JEE Main 2021 (Online) 16th March Morning Shift

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P $$ of magnitude 100 ...

JEE Main 2021 (Online) 24th February Evening Shift

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 c...

JEE Main 2020 (Online) 5th September Evening Slot

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...

JEE Main 2020 (Online) 5th September Morning Slot

A force $$\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$$ N acts at a point $$\left( {4\widehat i + 3\widehat j - \wide...

JEE Main 2020 (Online) 4th September Morning Slot

A circular disc of mass M and radius R is rotating about its axis with angular speed $${\omega _1}$$
. If another
stationary disc having radius $${R \...

JEE Main 2020 (Online) 3rd September Evening Slot

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...

JEE Main 2020 (Online) 3rd September Morning Slot

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 per...

JEE Main 2020 (Online) 9th January Morning Slot

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...

JEE Main 2020 (Online) 9th January Morning Slot

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 i...

JEE Main 2020 (Online) 7th January Evening Slot

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 m...

## MCQ (More than One Correct Answer)

JEE Main 2016 (Offline)

A particle of mass m is moving along the
side of a square of side ‘a’, with a uniform
speed v in the x-y plane as shown in the
figure :
Which of the ...