Question

Points P, Q and R are in a vertical line such that PQ = QR. A ball at P is allowed to fall freely. The ratio of times of descent through PQ and QR is

• A. 1:1
• B. $1:\sqrt{2}$
• C. $1:(\sqrt{2}-1)$
• D. $1:(\sqrt{2}+1)$

Answer 1

The correct option is C $1:(\sqrt{2}-1)$

Applying second equation of motion,

For $P$ to $Q-$

$h=0+\frac{1}{2}g{t}_1^2⟹t_1=\sqrt{\frac{2h}{g}}$

For $P$ to $R-$

$t_2=\sqrt{\frac{2\left(2h\right)}{g}}$

Time taken to descent $PQ=t_1=\sqrt{\frac{2h}{g}}$

Time taken to descent $QR=t_2-t_1=\sqrt{\frac{2h}{g}}(\sqrt{2}-1)$

Ratio $=1:(\sqrt{2}-1)$