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

Answer 1

The Correct Option is A

As track is frictionless, so total mechanical energy will remain constant
$T.M.E_I = T.M.E_F$
$ 0 + mgh = \frac{1}{2} mv_L^2 + 0$
$ h = \frac{v_L^2}{2g}$
For completing the vertical circle, $v_L \geq \sqrt{5 g\, R}$
$ h = \frac{5g \,R}{2g} = \frac{5}{2} R = \frac{5}{4} D $