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

Options

A. `(3)/(5)`
B. `(9)/(25)`
C. `(2)/(5)`
D. `(16)/(25)`

Answer

C

Explanation

Downward motion `v^(2) -0^(2) = 2 xx 9.8 xx 5 rArr v= sqrt98 = 9.9`
Also for upward motion
`0^(2)- u^(2) = 2 xx (-9.8) xx 1.8 rArr u = sqrt(3528) = 5.94`
Fractional loss `=(9.9-5.94)/(9.9) = 0.4`