Question

A ball of mass $2g$ released from the top of an inclined plane describes a circular motion of radius $20cm$ in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is:

• A. $20cm$
• B. $10cm$
• C. $50cm$
• D. $60cm$

Answer 1

Answer: (C)

The motion of ball is as shown below

At bottom of incline (at $P$ ) the potential energy of ball is converted into kinetic energy i.e..
$\frac{1}{2}m{v}^2=mgh$
$\Rightarrow v=\sqrt{2gh}\dots ..(i)$
To complete the vertical circle,
the velocity of ball should be at least $\sqrt{5gR}$.
$\Rightarrow v\ge \sqrt{5gR}$
$\sqrt{2gh}\ge \sqrt{5gR}$ [From Eq. (i)]
$\Rightarrow h\ge \frac{5}{2}R$
or $h_{\min }=\frac{5}{2}\times 20=50cm$