A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is nearly [2021]

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Solution

Q.
A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $(g = 10 {m/s}^{2})$ nearly [2021]

1 1.4 kg m/s

2 0 kg m/s

3 4.2 kg m/s

4 2.1 kg m/s

Ans.
(3)

Mass, $m = 0.15 kg; h_{1} = 10 m, h_{2} = 10 m; g = 10 m / s^{2}$

The velocity at the time of strike when going downwards.

$v = - \sqrt{2 g h_{1}}$

and when moving up $v' = \sqrt{2 g h_{2}}$

Impulse = change in momentum $m v' - m v = 2 m v$ (As $h_{1} = h_{2}$ )

$= 2 \times 0.15 \times \sqrt{2 \times 10 \times 10} = 4.2 kg$ $m / s$

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