question_answer

A simple pendulum is released from A as shown. If m and I represent the mass of the bob and length of the pendulum, the gain in kinetic energy at B is

A)  \[\frac{mgl}{2}\]                             

B)  \[\frac{mgl}{\sqrt{2}}\]

C)         \[\frac{\sqrt{3}}{2}mgl\]             

D)         \[\frac{2}{\sqrt{3}}mgl\]

E)  \[mgl\]

Correct Answer: C

Solution :

Loss of potential energy in coming from A to \[B=mgh\] \[=mgl\,cos30{}^\circ \]                 \[=\frac{\sqrt{3}}{2}mgl\] Kinetic energy gained = loss of potential energy                 \[=\frac{\sqrt{3}}{2}mgl\]