A frictionless track ABCDE ends in a circular loop of radius R .A body slides down track from point

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5.Work, Energy, Power and Collision

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A frictionless track $ABCDE$ ends in a circular loop of radius $R$ .A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is .................. $\mathrm{cm}$

A

$5$

B

$3.75$

C

$\frac{10}{3}$

D

$2$

Solution

for a complete loop velocity at $B$ should be greater than equal to $=\sqrt{5 \mathrm{gR}}$

$\mathrm{V}_{\mathrm{B}} \geq \sqrt{5 \mathrm{gR}}$

$\sqrt{2 \mathrm{gh}} \geq \sqrt{5 \mathrm{gR}}$

$\mathrm{R} \leq \frac{2 \mathrm{h}}{5}$

$\mathrm{R}_{\max }=\frac{2 \mathrm{h}}{5}=2 \mathrm{cm}$

Standard 11

Physics

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