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A block of mass 'm' is released on a smooth fixed incline plane at t = 0. The spring shown is ideal. The block touches the spring for the first time at $t = t_{1}$ with speed $v_{0}$ . The block returns to initial position of the release for the first time at $t = t_{2}$ .Then the number of times speed of the block becomes $v_{0}$ in $t = 0 t o t = t_{2}$ is

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answer is 4.

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Detailed Solution

Potential energy (Spring + Gravitational) with position is as shown

The above graph is traversed twice (back and forth) so, $v_{0}$ is achieved four times.

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