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 curved track 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 $\frac{5}{4}D$

Minimum velocity at bottom for completing the loop is $v=\sqrt{\frac{5gD}{2}}$

Applying work energy theorem between top and bottom of curved track
$mgh=\frac{1}{2}m{v}^2$
$mgh=\frac{1}{2}m(\sqrt{\frac{5gD}{2}}{)}^2$
$mgh=\frac{1}{2}m\frac{5gD}{2}\Rightarrow h=\frac{5D}{4}$