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A small ball of mass $m$ is released from rest at a height $h_{1}$ above ground at time $t = 0$ . At time $t = t_{0}$ , the ball again comes to rest at a height $h_{2}$ above ground. Consider the ground to be perfectly rigid and neglect air friction. In the time interval from $t = 0$ to $t = t_{0}$ , pick up the correct statements.

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Work done by gravity on ball is $m g (h_{1} - h_{2})$

Work done by ground on ball for duration of contact is $m g (h_{1} - h_{2}) .$

Average acceleration of the ball is zero.

Net work done on the ball by all forces except gravity is $m g (h_{1} - h_{2}) .$

answer is A, C, D.

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Detailed Solution

From the figure-l work done by gravity from $t = 0$ to $t = t_{0}$ is $W = mg$ $\times D i s p l a c e m e n t = m g (h_{1} - h_{2})$

Since initial and final velocity of ball is zero its average acceleration will be zero.
Net work done is zero from time interval $t = 0$ to $t = t_{0}$ . Hence $W_{c} + W_{n c} = 0 \Rightarrow W_{n c} = - W_{c} = m g (h_{1} - h_{2})$

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