Question

A thin uniform rod of length $l=60cm$ is oscillating about an axis passing through its one end in vertical plane. If rod is released from extreme position, then time required by rod to become vertical will be

• A. $\pi /5s$
• B. $\pi /6s$
• C. $\pi /8s$
• D. $\pi /10s$

Answer 1

The correct option is D $\pi /10s$

The time period is given by:
$T=2\pi \sqrt{\frac{I}{mgd}}T=2\pi \sqrt{\frac{m{l}^2}{3mgl/2}}=2\pi \sqrt{\frac{2l}{3g}}$

$=2\pi \sqrt{\frac{2\times 0.6}{3\times 10}}$
$=2\pi \sqrt{\frac{0.4}{10}}=2\pi \sqrt{0.04}$
$=2\pi \times 0.2$
$=\frac{4\pi }{10}$
time required $=T/4=\pi /10\text{sec}$