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A rubber ball is dropped from a height o...

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

A

`(16)/(25)`

B

`(2)/(5)`

C

`(3)/(5)`

D

`(9)/(25)`

Text Solution

Verified by Experts

The correct Answer is:
B
According to principle of conservation of energy Loss in potential energy =Gain in kinetic energy
`impliesmgh=(1)/(2)mv^(2)impliesv=sqrt(2gh)`
If `h_(1)` and `h_(2)` are initial and final heights ,then
`v_(1)=sqrt(2gh_(l)),v_(2)=sqrt(2gh_(2))`
Loss in velocity
`Deltav=v_(1)-v_(2)=sqrt(2gh_(l))-sqrt(2gh_(2))`
`therefore` Fractional loss in velocity
`=(Deltav)/(v_(l))=(sqrt(2gh_(l))-sqrt(2gh_(2)))/(2sqrt(2gh_(l)))=1-sqrt((h_(2))/(h_(1))`)
`1-sqrt((1.8)/(5))=1-sqrt(0.36)=1-0.6=0.4=(2)/(5)`
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