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Question: A rubber ball is dropped from a height of \(5m\) on a planet where the acceleration due to gravity i...

A rubber ball is dropped from a height of 5m5m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8m1.8m. The ball loses its velocity on bouncing by a factor of

A

16/25

B

2/5

C

3/5

D

9/25

Answer

3/5

Explanation

Solution

If ball falls from height h1, then it collides with ground with speed v1=2gh1v_{1} = \sqrt{2gh_{1}} …..(i)

and if it rebound with velocity v2, then it goes upto height h2 from ground, v2=2gh2v_{2} = \sqrt{2gh_{2}} …..(ii)

From (i) and (ii) v2v1=2gh22gh1=h2h1=1.85=925=35\frac{v_{2}}{v_{1}} = \sqrt{\frac{2gh_{2}}{2gh_{1}}} = \sqrt{\frac{h_{2}}{h_{1}}} = \sqrt{\frac{1.8}{5}} = \sqrt{\frac{9}{25}} = \frac{3}{5}