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 reset 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

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$lmg=\frac{m{v}^2}{l}$
$V=\sqrt{gl}$
$So,E_1=E_2$
$\frac{1}{2}M{V_1}^2=mgl+\frac{1}{2}M{V}^2$
$V_1=\sqrt{2gl}$
$mgh=\frac{1}{2}m{v}^2$
$mgh=\frac{1}{2}m\left(2gl\right)$
$h=1$