Question

A pendulum of length $10cm$ is hanged by a wall making an angle $3^{\circ }$ with vertical. It is swung to position $B$ . Time period of pendulum will be

• A. $\frac{\pi }{5}s$
• B. $\frac{2\pi }{15}s$
• C. $\frac{\pi }{6}s$
• D. subsequent motion will not be periodic

Answer 1

Answer: (B)

Let $T=2\pi \sqrt{\frac{l}{g}}$
$T=2\pi \sqrt{\frac{0.1}{10}}=\frac{\pi }{5}\text{s}$
Time taken by the pendulum in going from $A$ to $B=\frac{T}{4}$
Time taken by the pendulum in going from $A$ to $C=\frac{T}{12}$
$\therefore$ The time period of the pendulum $=2\left(\frac{T}{4}+\frac{T}{12}\right)=\frac{2T}{3}=\frac{2}{3}.\frac{\pi }{5}=\frac{2\pi }{15}s$