A body is dropped from a height `h`. If `t_1 and t_2` be the times in covering first half and the next distances respectively, then the relation between `t_1 and t_2` is.

Options

A. `t_1 = t_2`
B. `t_1 = 2t_2`
C. `t_1 = 3t_2`
D. `t_1 = (t_2)/((sqrt(2) - 1))`

Answer

D

Explanation

`t_1 = sqrt((2(h//2))/(g)) = sqrt((h)/(g)) rArr t_1 + t_2 = sqrt((2h)/(g))`
`rArr t_2 = sqrt((2h)/(g)) - t_1 = (sqrt(2 ) - 1) sqrt((h)/(g))`
`rArr (t_1)/(t_2) = (1)/(sqrt(2) - 1) rArr t_1 = (t_2)/(sqrt(2) -1)`.