Let A, B, C, D be points on a vertical line such that AB = BC = CD. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio.

Options

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

Answer

D

Explanation

`t_(1)=sqrt((2h)/g)`
`t_(2)=sqrt((2xx2h)/g)`
`t_(3)=sqrt((2xx3h)/g)`
Required ratio `t_(1) : (t_(2)-t_(1)) : (t_(3)-t_(2))`
`=1 : (sqrt(2)-1) : (sqrt(3)-sqrt(2))`