Question

A square metal frame in the vertical plane is hinged at O at its centre as shown in the figure A bug moves along the rod PN which is at a distance $\iota$ from the hinge such that the whole frame is always stationary even through the frame is free to rotate in the vertical plane about the hinge Then the motion of the bug will be simple harmonic with time period

• A. $2\pi \sqrt{\frac{\iota }{g}}$
• B. $2\pi \sqrt{\frac{2\iota }{g}}$
• C. $2\pi \sqrt{\frac{4\iota }{g}}$
• D. $2\pi \sqrt{\frac{\iota }{2g}}$

Answer 1

The correct option is A $2\pi \sqrt{\frac{\iota }{g}}$

Sol:

This syetem can be thought as equivalent to a Pendulum system.

Time period of pendulum $=2\pi \sqrt{\frac{l}{g}}$

Here, time poiod for bug $=2\pi \sqrt{\frac{\tau }{g}}$