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?
Figure

Answer 1

Minimum horizontal velocity should the block be given so that it moves in a complete vertical circle is $2 \sqrt{g l}$

Explanation:

At the point, the velocity is denoted as v. Let us assume that the block has the lower end, whose potential energy is zero.

The total energy is shown as $E = 0 + 1/2mv^{2}$

$E = \frac{1}{2} mv^{2}$

The potential energy at the maximum point will be (mg)2l.

It is written as below by the use of the law of conservation of energy,

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

$\begin{aligned}&v^{2}=4 g l\\&v=2 \sqrt{g l}\end{aligned}$

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