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  4. A particle has velocity √3 r g at the highest point in vertical circle. Find the ratio of tensions at the highest and lowest point

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Q. A particle has velocity $\sqrt{3 r g}$ at the highest point in vertical circle. Find the ratio of tensions at the highest and lowest point

NTA AbhyasNTA Abhyas 2022

Solution:

In vertical circular motin tension at top is mg - mv2/r and tension at bottom is mg + mv2/r

$T_{t o p}=\frac{m v^{2}}{r}-mg=2mg$
$\frac{T_{t o p}}{T_{b o t t o m}}=\frac{2 m g}{2 m g + 6 m g}=\frac{1}{4}$