# A particle is released from rest from a tower of height 3h, the ratio of time of fall for equal heights h ie $t_1:t_2:t_3$ is

$(a)\;\sqrt 3:\sqrt 2:1 \quad (b)\;3:2:1 \quad (c)\;9:4:1 \quad (d)\;1:(\sqrt 2-1):(\sqrt 3-\sqrt 2)$

$h=\large\frac{1}{2}$$gt_1^2 2h=\large\frac{1}{2}$$g(t_1+t_2)^2$
$3h=\large\frac{1}{2}$$g(t_1+t_2+t_3)^2$
$t_1 :(t_1+t_2):(t_1+t_2+t_3)=1 : \sqrt 2:\sqrt 3$
or $t_1 :t_2:t_3=1:(\sqrt 2-1):(\sqrt 3-\sqrt 2)$
Hence d is the correct answer.

edited Jan 26, 2014 by meena.p