A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by

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Solution

Q.
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8$ $m / s^{2}$ ) [2024]

1 4.32 kg ${ms}^{- 1}$

2 43.2 kg ${ms}^{- 1}$

3 23.9 kg ${ms}^{- 1}$

4 2.39 kg ${ms}^{- 1}$

Ans.
(4)

$m = 100 g = 0.1 kg, h_{1} = 10 m, h_{2} = 5 m$

$u = \sqrt{2 g h_{1}} = \sqrt{2 \times 98} m/s$

$v = \sqrt{2 g h_{2}} = \sqrt{98} m/s$

Impulse $= Δ \vec{P} = {\vec{P}}_{f} - {\vec{P}}_{i}$

$= 0.1 [\sqrt{98} + \sqrt{2 \times 98}]$

$\approx 2.39 kg m/s$

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