The ratio of time taken by two objects A and B of masses 1 kg and 3 kg to free fall from height 16 m and 25 m respectively is ......

Options

A. `12/5`
B. `5/12`
C. `4/5`
D. `5/4`

Answer

C

Explanation

`d = v _(0) t + 1/2 g t ^(2) and v _(0) = 0`
`therefore d = 1/2 g t ^(2)`
`t = sqrt ((2d)/(g))` it is independent of mass
`therefore t _(1) = sqrt ((2 xx 16)/(9.8)) and t _(2) = sqrt ((2 xx 25)/(9.8))`
`therefore (t_(1))/(t_(2)) = sqrt (( 2 xx 16)/(2 xx 2 5)) = 4/5`