Question

A ball of mass $m$ is attached to one end of a light rod of length $l$, the other end being hinged. What minimum velocity $u$ should be imparted to the ball downwards, so that it can complete the circle?

• A. $\sqrt{gl}$
• B. $\sqrt{5gl}$
• C. $\sqrt{3gl}$
• D. $\sqrt{2gl}$

Answer 1

The correct option is D $\sqrt{2gl}$


In the critical case, velocity at topmost point should be zero.
i.e. $v=0$
Let the hinged point be the datum line
Applying the conservation of mechanical energy, we get
$\frac{1}{2}m{u}^2+0=\frac{1}{2}m{v}^2+mgh$
where height from the datum or reference line is $l$,
$⟹v^2=u^2-2gl$
Putting the value of $v=0$, we get
$⟹0=u^2-2gl$
$⟹u=\sqrt{2gl}$

Hence option D is the correct answer