Question

A body is a allowed to slide down a frictionless track from rest position at its top under gravity. The track ends in a circular loop of diameter $D$. Then, the minimum height of the inclined track (in terms of $D$ ) so that it may complete successfully the loop is:

• A. $\frac{7D}{4}$
• B. $\frac{9D}{4}$
• C. $\frac{5D}{4}$
• D. $\frac{3D}{4}$

Answer 1

Answer: (C)

$\frac{5D}{4}$

$V_0$ required for a complete vertical circle: $V_0=\sqrt{\frac{5}{2}gD}$
WET between top and bottom:
$mgH=\frac{1}{2}m{V}_0^2$

$gH=\frac{5}{4}gD$

$H=\frac{5}{4}D$