Question

A small heavy block is attached to the lower end of a light rod of length $l$ which can be rotated about its clamped upper end. What minimum horizontal velocity should the block be given so that it moves in a complete vertical circle?

Answer 1

Let the velocity at the point is $v$ and assume that the lower end the potential energy of the block is zero.

The total energy is given as,

$E=\frac{1}{2}m{v}^2+0$

$E=\frac{1}{2}m{v}^2$

At the maximum point the potential energy will be $\left(mg\right)2l$.

By the law of conservation of energy, it can be written as,

$\frac{1}{2}m{v}^2=mg\times 2l$

$v^2=4gl$

$v=2\sqrt{gl}$

Thus, the minimum horizontal velocity is $2\sqrt{gl}$.