Ratio of Velocities Before and After Rebound – Rankers Physics

Collision: Practice Problem & Solution

A ball is dropped from a height of $5\text{ m}$, if it rebound upto height of $1.8\text{ m}$, then the ratio of velocities of the ball after and before rebound is: (1998)
$\frac{3}{5}$
$\frac{2}{5}$
$\frac{1}{5}$
$\frac{4}{5}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Collision. Understanding the underlying formula is key to arriving at the correct answer below:

The velocity before rebound is $v_1 = \sqrt{2gh_1}$ and after rebound is $v_2 = \sqrt{2gh_2}$. The ratio is $\frac{v_2}{v_1} = \sqrt{\frac{h_2}{h_1}} = \sqrt{\frac{1.8}{5}} = \frac{3}{5}$.

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