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General Physics> A spherical ball falls from A height of 4...

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A spherical ball falls from A height of 400m along the slope and execute a vertical circular motion. Find the minimum radius of vertical circle so that the tension at the topmost position is minimum

RANJEET Choudhary , 7 Years ago

Grade 12

1 Answers

Eshan

Last Activity: 7 Years ago

Loss in gravitational energy will be equal to the gain in kinetic energy.

$\implies mgh=\dfrac{1}{2}mv^2 \implies v=\sqrt{2gh}=\sqrt{8000}m$
In the vertical circular motion, if tension in topmost point is minimum, the centripetal acceleration will be provided by the gravitational force on ball alone.
$\implies \dfrac{mv'^2}{R}=mg \implies v'=\sqrt{gR}$
During this motion, the loss in kinetic energy is equal to gain in gravitational potential energy.
$\implies mg(2R)=\dfrac{1}{2}mv^2-\dfrac{1}{2}mv'^2 \implies 2mgR=\dfrac{1}{2}m(8000-gR)$
$\implies R=\dfrac{8000}{5g}=160m$

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