Question

A nail is fixed at a point $P$ vertically below the point of suspension '$O$' of a simple pendulum of length $1m$. The bob is released when the string of pendulum makes an angle ${30}^0$ with horizontal. The bob reaches lowest point then describes vertical circle whose centre coincides with $P$. The least distance of $P$ from $O$ is:

• A. $0.4m$
• B. $0.5m$
• C. $0.6$
• D. $0.8m$

Answer 1

The correct option is D $0.8m$

Vol city of bob at lout point.
$V_o=\sqrt{2gh}=\sqrt{2gh(1-\frac{1}{2})}=\sqrt{g.}mvs.$
for completing the circle alout P , the $V_o=\sqrt{5gl}.$
$\therefore V_o=\sqrt{g}=\sqrt{5gl}.$
$l=\frac{1}{5}=0.2m$
$\therefore distancbetweenOP=1-0.2=0.8M$