Question

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

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

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}=m g h $
$\Rightarrow v=\sqrt{2 g h} \ldots . .( i )$
To complete the vertical circle,
the velocity of ball should be at least $\sqrt{5 g R}$.
$\Rightarrow v \geq \sqrt{5 g R} $
$\sqrt{2 g h} \geq \sqrt{5 g R} $ [From Eq. (i)]
$\Rightarrow h \geq \frac{5}{2} R$
or $ h_{\min }=\frac{5}{2} \times 20=50 \,cm$