A ball is thrown down a lawn in such a way that it initially slides with a speed `v_(0)` without rolling. It gradually picks up rotational motion. Prove that it will be without sliding, that is, its motion will be pure rolling when its speed falls to `5/7v_(0)`.

A ball is thrown down a lawn in such a way that it initially slides with a speed v_(0) without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping :

A heavy disc is thrown on a horizontal surface in such a way that it slides with a speed V_(0) intially without rollind . It will start rolling without slipping when its speed is reduced

A ball (solid sphere) is thrown down the valley in such a way that it slides with a speed v_(0) initially without rolling. Prove that it will roll without any sliding when its speed falls to (5/7)v_(0) . The transition from pure sliding to pure rolling is gradual, so that both sliding and rolling take place during this interval.

A heavy solid sphere is thrown on a horizontal rough surface with initial velocity u without rolling. What will be its speed, when it starts pure rolling motion ?

A sphereicla ball of mass M and radius R is projected along a rough horizontal surface so that initially (t=0) it slides with a linear speed v_(0) but does not rotate. As it slides, it begins to spin and eventually rolls without slipping. How long does it take to begin rolling without slipping?

A solid sphere is thrown on a horizontal rough surface with initial velocity of centre of mass V_0 without rolling. Velocity of its centre of mass when its starts pure rolling is

A billiard ball is struck by a cue when it starts moving with velocity v_(0) without rolling. How far will the ball move before it ceases to slide on the table if mu is the coefficient of friction between ball and table?

A thin hollow cylinder open at both ends and weight 5 kg (i) slides with a speed of 5m//s without rotating and (ii) rolls with the same speed without slipping. Compare the KE of the cylinder in the two cases.