A frictionless track ends in a vertical circular loop radius R. A body slides down the track from point A which is at a height 10cm. Maximum value of R for the body to successfully complete the loop is

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A frictionless track ends in a vertical circular loop radius R. A body slides down the track from point A which is at a height 10cm. Maximum value of R for the body to successfully complete the loop is

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$\frac{15}{4} c m$

$\frac{10}{3} c m$

$5 c m$

$4 c m$

answer is D.

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Detailed Solution

From the conservation of energy

$m g h = \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{2 g h} \sqrt{2 g h} = \sqrt{5 g R} R = \frac{2 \times 10}{5} = 4 c m$

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