Question

A body is allowed to slide down a frictionless track freely under gravity. The track end in a semicircular shaped part of a diameter O. The height (minimum) from which the body must fall so that it completes the circle, is

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

Answer 1

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

For the body to reach point B, the body must have least velocityof $\sqrt{5gr}$ at A. So for a body falling from height h.
Velocity $=\sqrt{2gh}$
$\sqrt{2gh}=\sqrt{5gr}\Rightarrow 2gh=5g\frac{D}{2}$
$h=\frac{5D}{4}$