A solid iron sphere A rolls down an inclined plane, while an identical hollow sphere B of same mass slides down the plane in a frictionless manner. At the bottom of the inclined plane, the total kinetic energy of sphere A is

less than that of B

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equal to that of B

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more than that of B

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sometimes more and sometimes less

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Solution

The correct option is A equal to that of B
Work-energy theorem, $W_{a l l f o r c e s} = Δ K . E$
Solid iron sphere will do translational as well as rotational motion and work done by friction force is zero due to pure rolling.
$m g h_{1} = K . E_{A} - 0 ⟹ K . E_{A} = m g h_{1}$
Hollow sphere will do only translational motion.
$m g h_{2} = K . E_{B} - 0 ⟹ K . E_{B} = m g h_{2}$
Thus $K . E_{A} = K . E_{B}$ for the same height of the inclined plane.

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