A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) jus

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

Accepted Answer

For a body to complete a vertical circle, the minimum velocity at the bottom of the circle is $\sqrt{5gR}$. Using conservation of energy, $mgh = \frac{1}{2}mv^2 = \frac{1}{2}m(5gR) = \frac{5}{2}mgR$. Since $D = 2R$, $h = \frac{5}{4}D$.

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