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  4. 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

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Q. 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 toPhysics Question Image

NEETNEET 2018Work, Energy and Power

Solution:

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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 $