A particle is released from rest from a tower of height 3h. The ratio of time intervals for fall of equal height 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

4

Explanation

`h=(1)/(2)g"t"_(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)`
`:.t_(1):t_(2):t_(3)=1:(sqrt(2)-1):(sqrt(3)-sqrt(2))`