Question

A body is allowed to slide down a frictionless track freely under gravity. The track ends in a semicircular shaped part of diameter D. What should be the minimum height from which the body must fall so that it completes the circle.

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

Answer 1

Answer: (B)

$\frac{5}{4}D$

Answer 2

For the body to complete the vertical circle, the speed at the bottom of the circular track must equal $\sqrt{5gR}$ , where R is the radius of the circle. If the body falls through a height h until it reaches the bottom of the track, $\sqrt{5g \frac{D}{2}}=\sqrt{2gh}$ (From energy conservation) or, $h=\frac{5D}{4}$