Question

The angle made by the string of a simple pendulum with the vertical depends on time as

$\theta =\frac{\pi }{90}sin\left[\right(\pi s^{-1}\left)t\right]$.Find the length of the pendulum if $g={\pi }^2\frac{m}{s^2}$.

• A. $\pi m$
• B. $\frac{1}{\pi }m$
• C. 1m
• D. $\frac{90}{\pi }m$

Answer 1

The correct option is C

1m

The given equation is $\theta =\frac{\pi }{90}sin\left[\right(\pi s^{-1}\left)t\right]$

Comparing it with standard equation of angular SHM $\theta =\theta {+}_{\circ }sin(\omega t+\varnothing )$

We se $\omega =\pi$

$\Rightarrow T=\frac{2\pi }{\omega }=\frac{2\pi }{\pi }=2d$

The time period of SHM is 2s

Also $T=2\pi \sqrt{\frac{l}{g}}$

$2=2\pi \times \sqrt{\frac{l}{{\pi }^2}}[giveng={\pi }^2]$

$\ell =1m$