Q. Two bodies are thrown vertically upwards with their initial speed in the ratio $2\ :3$. The ratio of the maximum heights reached by then and the ratio of their time taken by them to return back to the ground respectively are
A) $4\ \ :9$ and $2\ :3$
B) $2\ :3$ and $\sqrt{2}\ :\ \sqrt{3}$
C) $\sqrt{2}\ :\ \sqrt{3}$ and $4\ :9$
D) $\sqrt{2}\ :\ \sqrt{3}$ and $2\ :3$
Explanation
(a) $v = u - gt$
At max height $v^{2} = u^{2} - 2gh$
$t = \frac{u}{g}\ \ \ \ \ \ \ h = \frac{u^{2}}{2g}$
$\frac{t_{1}}{t_{2}} = \frac{2}{3}\ \ \ \ \ \frac{h_{1}}{h_{2}} = \left( \frac{2}{3} \right)^{2} = \frac{4}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.