In the following figure, a weight W is attached to a string wrapped round a solid cylinder of mass M mounted on a frictionless horizontal axle at O.

If the weight starts from rest and falls a distance h, then its speed at that instant is

A solid cylinder rolls down an inclined plane that has friction sufficient to prevent sliding. The ratio of rotational energy to total kinetic energy is

A swimmer while jumping into water from a height easily forms a loop in the air, if

Assertion : A ladder is more apt to slip when you are high up on it than when you just begin to climb

Reason : At the high point on a ladder, the torque is large and on climbing up the torque is small

An inclined plane makes an angle of $30°$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

Which of the following statements is correct?

A ball of mass m moving with velocity $v_0$ collides a wall as shown in the figure. After impact, it rebounds with a velocity $\frac{3}{4}{v}_0$. The impulse acting on ball during impact is 

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances traveled by A and B in the same time interval, then

If a gymnast, sitting on a rotating stool, with his arms outstretched, suddenly lowers his hands

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

A particle of mass m moves in the XY planewith a velocity of V along the straight line AB. If the angular momentum of the particle about the origin O is L_A when it is at A and L_B when it is at B, then

If rotational kinetic energy is 50 % of translational kinetic energy, then the body is 

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an acceleration

A solid sphere rolls without slipping down a $30°$ inclined plane. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, the acceleration of the rolling sphere is

If the equation for the displacement of a particle moving on a circular path is given by $\theta =2t^3+0.5$, where $\theta$ is in radian and t is in second, then the angular velocity of the particle after 2s is 

A pan containing a layer of uniform thickness of ice is placed on a circular turntable with its centre coinciding with the centre of the turn table. The turntable is now rotated at a constant angular velocity about a vertical axis passing through its centre and then driving is withdrawn. There is no friction between the table. As the ice melts

The motion of planets in the solar system is an example of the conservation of

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

A particle of mass 15 kg has an initial velocity ${\mathrm{v}}_{\mathrm{i}} = \hat{\mathrm{i}} - 2\hat{\mathrm{j}}$ m/s. It collides with another body and the impact time is 0.1 s, resulting in a velocity ${\mathrm{v}}_{\mathrm{f}} = 6\hat{\mathrm{i}} + 4\hat{\mathrm{j}} + 5\hat{\mathrm{k}}$ m/s after impact. The average force of impact on the particle is

Two Circular discs A and B are of equal masses and thicknesses but made of metal with densities ${\mathrm{d}}_{\mathrm{A}} \mathrm{and} {\mathrm{d}}_{\mathrm{B}}$ (${\mathrm{d}}_{\mathrm{A}} > {\mathrm{d}}_{\mathrm{B}}$). If their moments of inertia about an axis passing through their centers and perpendicular to circular faces be ${\mathrm{I}}_{\mathrm{A}} \mathrm{and} {\mathrm{I}}_{\mathrm{B}}$, then

A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to the translational kinetic energy. The body is 

A wheel with a radius of 20 cm has forces applied to it as shown in the figure. The torque produced by the forces of 4 N at A, 8N at B, 6 N at C, and 9N at D, at the angles indicated, is:
                    

The moment of inertia of a thin rectangular plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is 

The centre of a wheel rolling on a plane surface moves with a speed ${\mathrm{v}}_0$. A particle on the rim of the wheel at the same level as the centre will be moving at speed

Moment of inertia of a uniform cylinder of mass M, radius R and length l about an axis passing through its center and normal to its axis would be

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }}m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of

A wheel has angular acceleration of 3.0 rad/$se{c}^2$ and an initial angular speed of 2.00 rad/sec.  In a time of 2 sec it has rotated through an angle (in radian) of 

The bob A of a simple pendulum is released when the string makes an angle of 45 with the vertical. It hits another bob B of the same material and the same mass kept at rest on a table. If the collision is elastic