A body is allowed to fall freely under gravity from a height of 10 m. If it loses 25% of its energy on impact with the ground, to what height will it rise after one impact? 

Options

A. 2.5 m
B. 5.0 m
C. 7.5 m
D. 9.0 m

Answer

C

Explanation

Height `h = 10 m`. Potential energy at this height = mgh. On reaching the ground, KE = mgh. Since the body loses 25% of energy due to impact, kinetic energy of the body after one impact = 0.75 mgh. If `v_1` is the initial upward velocity after the impact , we have
`1/2 mv_1^2 = 0.75 mgh = 3/4 mgh " or " v_1^2 = 1.5 gh`
The height `h_1` to which the bocy will rise is
`h_1 = (v_1^2)/(2g) = (1.5gh )/(2g) = 0.75 h = 0.75 xx 10 = 7.5 m ( :. h = 10m). `