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  4. A body of mass m slides down an incline and reaches the bottom with a velocity v . If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been

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Q. A body of mass $m$ slides down an incline and reaches the bottom with a velocity $v$ . If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

When body slides, $v=\sqrt{2 g h} \, $ ....(1)
When ring rolls, $v′=\sqrt{\frac{2 g h}{1 + k^{2} / r^{2}}}=\sqrt{\frac{2 g h}{2}}=\frac{v}{\sqrt{2}}$