A solid cylinder (SC),Hollow cylinder (HC)& solid sphere (SS)of same mass & radii are released simultaneously from the same height on an incline. The order in which they will reach the bottom is (From least time to most time order)

A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity $v=a+{ bt }^{ 2 }$. If the cylinder is not allowed to slip then the time when the cylinder is about to topple, will be equal to

A solid cylinder of mass 2 kg rolls down an inclined plane from a height of 4 cm. Its rotational kinetic energy when it reaches the foot of the plane is (g = 10 ${ m/s }^{ 2 })$

A disc of radius R rolls on a horizontal surface with linear velocity $ \overrightarrow {v} = v \hat {i} $ and angular velocity $ \overrightarrow {\omega} = - \omega \hat k $ there is a particle P on the circumference of the disc which has velocity in vertical direction. the height of that particle from the ground will be

A wheel of mass M and radius a and M.I. $I _G$ (about centre of mass) is set rolling with angular velocity $\omega$ up a rough inclined plane of inclination $\theta$. The distance travelled by it up the plane is :

A disc of mass $m$ of radius $r$ is placed on a rough horizontal surface. A cue of mass $m$ hits the disc at a height $h$ from the axis passing through centre and parallel to the surface. The cue stop and falls down after impact. The disc starts pure rolling for

A uniform rigid rod has length $L$ and mass $m$. It lies on a horizontal smooth surface, and is rotated at a uniform angular velocity $\omega$ about a vertical axle passing through one of its ends. The force exerted by the axle on the rod will be

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 gets to the bottom of the plane first?

A body is given translational velocity and kept on a surface that has sufficient friction. Then:

(a) A child stands at the center of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of $40$ rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to $2/5$ times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?