Question

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

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

Answer 1

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

Let total energy is conserved,

Total mechanical energy at start = Total mechanical energy at 'B'

mgh = $\frac{1}{2}m{v}_B^2+mgD$ ...........(1)

Minimum speed required to complete rotation is, $v_b=\sqrt{rg}=\sqrt{Dg/2}$

Hence equation (1) becomes,

mgh = $\frac{1}{2}m\frac{D}{2}g$ + mgD

hence, $h=\frac{5D}{4}$