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?
Figure

Answer 1

The minimum value of h so that the block moves in a complete circle about the ring is l.

Explanation:

Here the rod is fixed rigidly to the block,  

At the top of the ring is equal to l.

Now, Total energy = Kinetic energy + Potential energy

                              $=\frac{1}{2} m v^{2}+m g l$

At height h, the total energy potential

                        $\mathrm{P.E}=\mathrm{mgh}$

Now, we get to compare these two equations,

                       $m g h=\frac{1}{2} m v^{2}+m g l$      

                            $h=\frac{1}{2 g} v^{2}+l$            

l will be the minimum when v =0 , ∵ l is fixed  

Now, v value is set in above equation

                             h = 0+l

                             h = l

The minimum value is therefore l.

Answer 2

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