Rotational Motion · Physics · JEE Main

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...

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...

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...

Three balls of masses $$2 \mathrm{~kg}, 4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ respectively are arranged at centre of the edges of an equilateral tri...

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 $$\fra...

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...

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...

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...

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...

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...

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...

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 ...

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 / ...

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...

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 ...

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...

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...

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...

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

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

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}...

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{...

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...

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...

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...

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...

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 ...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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

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 (...

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

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 ...

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 ...

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 ...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 ______...

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...

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...

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...

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...

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...

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...

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 ...

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...

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...

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...

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 \...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 fig...

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...

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 ...

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...

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...

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....

Match List-I with List-II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family...

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 solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the...

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 ...

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$...

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...

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

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...

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...

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...

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)...

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...

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...

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...

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

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...

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...

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...

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 ...

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 ...

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...

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...

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 ...

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...

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...

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

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...

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...

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...

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...

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...

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 (...

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...

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...

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

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 ...

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...

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 ...

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 ...

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...

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...

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...

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...

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...

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}...

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. ...

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...

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...

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...

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

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...

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...

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 ...

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,...

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...

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...

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 ...

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...

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...

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...

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...

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...

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 ...

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...

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 ...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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 :

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 : ...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 ...

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

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...

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...

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...

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...

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...

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...

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...

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 ...

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...

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...

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) ...

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...

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 $$\...

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...

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 ...

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

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

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 ...

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...

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

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...

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...

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...

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 ?

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

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

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...

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...

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

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

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...

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 ...