Q. Two particles held at different heights $a$ and $b$ above the ground are allowed to fall from rest. The ratio of their velocities on reaching the ground is
A) $a\ :b$
B) $\sqrt{a}:\sqrt{b}$
C) $a^{2}:b^{2}$
D) $a^{3}:b^{3}$
Explanation
(b) $v \propto \sqrt{h}$ $\therefore\frac{v_{1}}{v_{2}} = \sqrt{\frac{a}{b}}$
So, (b) is the correct choice.
The velocity acquired by a body in falling freely from rest through height $h$ is $\sqrt{2gh.}$
[$u = 0,v = ?,^{'}a^{'} = g,\ 'S^{'} = h,v^{2} - u^{2} = 2aS$]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.