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 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

Now Total energy = Kinetic energy + Potential energy,

$=1/2m{v}^2+mgl----\left(i\right)$

at height $h$. The Potential energy due to total energy $P.E=mgh----\left(ii\right)$

Now equating these two equation we get,

$mgh=1/2m{v}^2+mgl$

$h=\frac{1}{2g}\left(v^2\right)+l----\left(iii\right)$

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

Now putting $v$ value in above equation

$h=0+1$

$h=1$

Hence the minimum value is $l$.