A solid sphere rolls down an inclined plane and its velocity at the bottom is v1

Question

A solid sphere rolls down an inclined plane and its velocity at the bottom is

v_{1}

. Then same sphere slides down the plane (without friction) and let its velocity at the bottom be

v_{2}

. Which of the following relation is correct

Options:

A . v1=v2

B . v1=57v2

C . v1=75v2

D . None of these

Answer: Option D
:
D
When solid sphere rolls down an inclined plane the velocity at bottom

v_{1} = \sqrt{\frac{10}{7} g h}

but, if there is no friction then it slides on inclined plane and the velocity at bottom

v_{2} = \sqrt{2 g h}

∴ \frac{v_{1}}{v_{2}} = \sqrt{\frac{5}{7}} .

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