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

Options

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

Answer

B

Explanation

A ball dropped from a height `h_1` on reaching the planet.s surface will have a velocity given by `v_1 = sqrt(2gh_1)`
Let `v_2` be the velocity with which the ball boụnes. It will attain a height `h_2` given by
`v_2^2 = sqrt(2gh_2) therefore (v_2)/(v_1) = sqrt((h_2)/(h_1)) = sqrt((1.8)/(5)) = 0.6 " or " 1 - (v_2)/(v_1) = 1 - 0.6 " or " (v_1 - v_2)/(v_1) = 0.4 = 2/5`