A particle is released from rest from a tower of height `3h`. The ratio of times of times to fall equal heights `h,` i.e. `t_(1):t_(2):t_(3)` is

Options

A. `sqrt(3):sqrt(2):1`
B. `3:2:1`
C. `9:4:1`
D. `1:(sqrt(2)-1):(sqrt(3)-sqrt(2))`

Answer

D

Explanation

A particle ……….
`h = (1)/(2)"gt"_(1)^(2) 2h=(1)/(2)g(t_(1)+t_(2))^(2)3h`
`= (1)/(2)g(t_(1)+t_(2)+t_(3))^(2)`
`:. T_(1):(t_(1)+t_(2)): (t_(1)+t_(2)+t_(3)) = 1: sqrt(2): sqrt(3)`
`implies t_(1) : t_(2) : t_(3) = 1: (sqrt(2)-1) : (sqrt(3)-sqrt(2))`