1.

A ball is thrown vertically downwards from a height of 20m with an intial velocity `v_(0)`. It collides with the ground, loses 50% of its energy in collision and rebounds to the same height. The intial velocity `v_(0)` is (Take, g =10 `ms^(-2)`)A. `14ms^(-1)`B. `20ms^(-1)`C. `28ms^(-1)`D. `10ms^(-1)`

Answer» Correct Answer - b
(b) Suppose a ball rebounds with speed v,
`v=sqrt(2gh)=sqrt(2xx10xx20)`
`=20m//s`
Energy of a ball just after rebound,
`E=(1)/(2)mv^(2)=200m`
As, 50% of energy loses in collision means just before collision energy is 400 m.
According to law of conservation of energy, we have
`(1)/(2)mv_(0)^(2)+mgh=400m`
`implies (1)/(2)mv_(0)^(2)+mxx10xx20=400m`
`implies v_(0)=20m//s`


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