Question

Figure (8-E14) 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?

Answer 1

The rod is rigidly attached to the block , At the highest point ring will equal to $l$ .

Now

Total energy = Kinetic energy + Potential energy.

$1/2mv²+mgl----\left(i\right)$

At height $h$. The Potential energy due to total energy

$P.E=mgh-------\left(ii\right)$

Now equating these two equations and get,

$mgh=1/2mv²+mgl$

will be the minimum when $v=0$ , $\because l$ is fixed

Now,

putting $v$ value in above equation

Hence, the minimum value is $l$ .