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?

after releasing the system , heavy block moves in the influence of gravity & gains some speed ...there is no tension in rod...

after covering H distance , rod & particle are horizontally in same level with ring ....now tension is present as the hook gets into the ring...

now block moves in circle .... let at this point potential is 0 ...

now applying energy conservation bw the topmost point of circle & initial point ...

mv²/2 + 0 = mv₁²/2 + mgL           (v = initial speed , v₁ final speed)

mv²/2 = mgH , so

mgH - mgL = mv₁²/2                        ....................1

at final state ,let T is tension then

T+mg = mv₁² /L    (centripital force)

 if tension is 0 then also block can complete the circle so

mv₁² = mgL  ................2

using 1 & 2

mgH = mg(3L/2)

H = 3L/2

approve my ans if u like it

Approved