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 bod

Question

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 )

TestHub · Accepted Answer

Using equation of motion with constant acceleration, we can write:

$v_{1} = \sqrt{2 g h_{1}}$ and $v_{2} = \sqrt{2 g h_{2}}$

Now, required impulse

$\vec{I} = Δ \vec{p} = {\vec{p}}_{f} - {\vec{p}}_{i}$

Given, $M = 0.1 kg$

Therefore,

$I = Δ p = 0.1 (\sqrt{2 \times 9.8 \times 5} - (- \sqrt{2 \times 9.8 \times 10}))$

$= 0.1 (7 \sqrt{2} + 14) \approx 2.39 kg m s^{- 1}$

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