Question

Figure shows a light rod of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of h so that the block moves in a complete circle about the ring?

• A. h = l
• B. h = 3l
• C. h = 2l
• D. h = 4l

Answer 1

The correct option is A

h = l

The minimum velocity required to make the block complete circle $(\because v_{top}=0)$

$\frac{1}{2}m(v_{min}{)}^2=2mgl$

$v_{min}=2\sqrt{gl}$

Conserving energy from point A to C as only conservative force gravity mg(h + l) = $\frac{1}{2}m4gl$

h = l