Question

A bob of mass m is suspended by a massless string of length I. The horizontal velocity v at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies

• A. $\theta =\frac{\pi }{4}$
• B. $\frac{\pi }{4}$ < $\theta$ < $\frac{\pi }{2}$
• C. $\frac{\pi }{2}$ < $\theta$ < $\frac{3\pi }{4}$
• D. $\frac{3\pi }{4}$ < $\theta$ < $\pi$

Answer 1

The correct option is D $\frac{3\pi }{4}$ < $\theta$ < $\pi$


$v=\sqrt{5hl}$ [At position 'A']
$l^1=lsin{\theta }^1$
Applying conservation of energy
$mg(l+lsin{\theta }^1)+\frac{1}{2}m\frac{59l}{4}=\frac{m}{2}\left(5gl\right)\Rightarrow sin{\theta }^1=\frac{7}{8}\Rightarrow {\theta }^1>\frac{\pi }{4}\therefore \theta =(90+{\theta }^1)\Rightarrow \theta >\frac{3\pi }{4}but\theta <\pi$