An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

The distance covered by a body of mass 5 g having linear momentum 0.3 kg m/s in 5 s is

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in...

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the...

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration ...

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90$$^\circ$$ sector is removed. The moment of inertia of the remaining part ...

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and anoth...

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.The centre of mass of...

Find the torque about the origin when a force of 3 $$\hat j$$ N acts on a particle whose position vector is 2 $$\hat k$$ m.

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2$$\pi $$ revolutions...

Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respecitively. Their time pe...

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) si...

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the fol...

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with ...

The moment of the force, $$\overrightarrow F = 4\widehat i + 5\widehat j - 6\widehat k$$ at (2, 0, –3), about the point (2, –2, –2), is given by

Which of the following statements are correct ? (1)   Centre of mass of a body always coincides with the centre of gravity of the body...

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a ...

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular veloc...

Two rotating bodies A and B of masses m and 2m with moments of inertia $${I_A}$$ and $${I_B}$$ ($${I_B}$$ > $${I_A}$$) have equal kinetic energy ...

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometr...

A light rod of length $$l$$ has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the ...

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects ...

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the re...

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is...

An automobile moves on a road with a speed of 54 km h$$-$$1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis ...

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis pe...

A force $$\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k$$ is acting at a point $$\overrightarrow r = 2\widehat i - 6\widehat j -...

A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d fro...

A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smoot...

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and ...

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one en...

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $$\theta $$ without slipping and slipping dow...

The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and pe...

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and ...

A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of $${{3{v^2}} \over {4g}}$...

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is...

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initia...

A car of mass m is moving on a level circular track of radius R. If $$\mu $$s represents the static friction between the road and tyres of the car, th...

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through ...

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin i...

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weights 100 kg. The 55 kg ...

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45o, the speed of the car is ...

ABC is an equilateral triangle with O as its centre. $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ represent three ...

A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causin...

The instantaneous angular position of a point on a rotating wheel is given by the equation $$\theta \left( t \right) = 2{t^3} - 6{t^2}$$ The torque on...

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$I$$...

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $${R \over 3}$$ is removed concentrically. The moment of inertia of th...

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an incl...

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $$\omega $$. Two objects each of msass m are att...

A circular disk of moment of inertia $${I_t}$$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $${\omega _i}...

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any ...

A gramophone record is revolving with an angular velocity $$\omega $$. A coin is placed at a distance r from the centre of the record. The static coe...

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $$\...

Four identical thin rods each of mass M and length $$l$$, form a square frame. Moment of inertia of this frame about an axis through the centre of the...

If $$\overrightarrow F $$ is the force acting on a particle having position vector $$\overrightarrow r $$ and $$\overrightarrow \tau $$ be the torque...

Two bodies of mass 1 kg and 3 kg have position vectors $$\widehat i + 2\widehat j + \widehat k$$ and $$ - 3\widehat i - 2\widehat j + \widehat k$$, re...

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent ro...

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A uniform rod AB of length $$l$$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the ...

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to orig...

A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in...

A uniform rod AB of length $$l$$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the ...

The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal ...

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $$\theta $$. The frictional force

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their an...

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side $$l$$ cm (as shown in the figure). The momen...

A wheel having moment of inertia 2 kg m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's...

Consider a system of two particles having masses m1 and m2. If the particle of mass m1 is pushed towards the mass centre of particles through a distan...

A round disc of moment of inertia $$I$$2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of mome...

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about...

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. t...

A stone is tied to a string of length $$l$$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant o...

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mas...

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $$\omega $$. Four objects each of mass m, are ...

A rod of length is 3 m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from ...

A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel compl...

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum ...

A disc is rotating with angular speed $$\omega $$. If a child sits on it, what is conserved

A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with

A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct?

For the adjoining diagram, the correct relation between I1, I2, and I3 is, (I-moment of inertia) ...

For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier

As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which poin...