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A ball falls under gravity from a height...

A ball falls under gravity from a height of 10 m with an initial downward velocity u. It collides with the ground, losses 50% of its energy in collision and then rises back to the same height. The initial velocity u is

A

`7 m s^(-1)`

B

`25 m s^(-1)`

C

`14 m s^(-1)`

D

`28 m s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
If m is the mass of the ball, then its total initial energy at height h. `=1/2 m u^2 +mgh`
Energy after collision =50% of `(1/2 m u^2 +mgh)`
As the ball rebounds to height h, so
`1/2(1/2m u^2+mgh)=mgh or 1/4 m u^2=1/2mgh`
`u=sqrt(2gh)=sqrt(2xx9.8xx10)=14 ms^(-1)`
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