Question

A body slides down on a frictionless track which ends in a circular loop of diameter $D$ . The minimum height $h$ in terms of $D$ so that the body may just complete the circular loop, is

• A. $h=\frac{5}{2}D$
• B. $h=\frac{3}{2}D$
• C. $h=\frac{5}{4}D$
• D. $h=2D$

Answer 1

Answer: (C)

By conservation of energy,
$\frac{1}{2} m v^{2} = m g h$
$v = \sqrt{2 g h}$ ...(i)
For looping the loop, the lower velocity must be greater than $\sqrt{5 g r}$
$v_{min} = \sqrt{5 g r} = \sqrt{\frac{5 g D}{2}}$ ...(ii)
From equation (i) and (ii),
$2 g h = \frac{5 g D}{2}$
$h = \frac{5 D}{4}$