Question

When two particles each of mass $m$ are dropped from height h and $2h$ respectively, then the ratio of their times to reach the ground is

• A. $ 1:\sqrt{2} $
• B. $ \sqrt{2}:1 $
• C. $ 1:2 $
• D. $ 2:1 $

Answer 1

Answer: (A)

From relation
$h=u t +\frac{1}{2} g t^{2} \,\, $ (with $u=0)$,
we have $h=\frac{1}{2} g t^{2}$
$\Rightarrow t=\sqrt{\left(\frac{2 h}{g}\right)} \propto \sqrt{h}$
$\therefore \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{1}}{h_{2}}} \sqrt{\left(\frac{h}{2 h}\right)}=\frac{1}{\sqrt{2}}$