Question

In a simple pendulum, the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes angle $\theta$ with the vertical:

• A. $\theta ={\sin }^{-1}\left(1/3\right)$
• B. $\theta ={\cos }^{-1}\left(\frac{2}{3}\right)$
• C. $\theta ={60}^o$
• D. $\theta =0^o$

Answer 1

The correct option is B $\theta ={\cos }^{-1}\left(\frac{2}{3}\right)$

The correct option is B

Given,

A simple pendulum.

Tension $=T$. Angle with vertical = $\theta$.

Speed of pendulum$=vat\theta$.

Length of string $=L$

$T=mgcos\theta +\frac{m{v}^2}{L}$

$\frac{m{v}^2}{2}=KE=mgLcos\theta$ (loss in PE).

By Solving these, $T=3mgcos\theta$.

When the string snaps, $T=2mg$.

So $cos\theta =\frac{2}{3}$

$\theta =co{s}^{-1}\frac{2}{3}$