Question

A body initially at rest begins to slid 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 $\frac{5}{4}D$

Total energy is conserved,
Total mechanical energy at $A$ = 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, $h=\frac{5D}{4}$