Question

A body is allowed to slide on a frictionless track from rest position under gravity. The track ends into a circular loop of diameter $D$. What should be the minimum height of the body in terms of $D$ so that it may complete the loop successfully?

• A. $\frac{4}{5}D$
• B. $\frac{5}{4}D$
• C. $1D$
• D. $2D$

Answer 1

The correct option is B $\frac{5}{4}D$

For the body to reach point $B$, the body must have least velocity of $\sqrt{5gR}$ [From vertical circular motion] at A.
So, for a body falling from height $h$
Velocity $\left[V\right]=\sqrt{2gH}$
$\sqrt{2gh}=\sqrt{5gr}$
$[\text{As}r=\frac{D}{2}]$
$\sqrt{2gh}=\sqrt{\frac{5gD}{2}}$
$h=\frac{5D}{4}$