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 ?

Answer 1

Here 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 ----(i)

at height h , The Potential energy due to total energy
P.E = mgh    -------(ii)

Now equating these two equation we get,
mgh = 1/2mv² + mgl
$h = \frac{1}{2g} ( v^2) +l$ -----(iii)

 $l$ will be the minimum when v =0 , ∵ l is fixed 
Now putting v value in above equation
$h =0 + l$
$h = l$ .

Hence the minimum value is l .



Hope it Helps.

Answer 2

Answer:

at the highest point☝️☝️