Question

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes as vertical of diameter $AB=D$. The height $h$ is equal to:

• A. $\frac{3}{2}D$
• B. $D$
• C. $\frac{5}{4}D$
• D. $\frac{7}{5}D$

Answer 1

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

Given: a body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes as vertical of diameter AB=D.

To find the height h

Solution:

Energy conservative forces

$K+U=E$ Here E is constant

$\Delta K+\Delta U=0⟹\Delta K=-\Delta U$

For particles to complete circle

$V=\sqrt{5gR}⟹V=\sqrt{gh}⟹\sqrt{2gh}=\sqrt{\frac{5gD}{2}}⟹2gh=\frac{5gD}{2}⟹h=\frac{5D}{4}$

is the height h.