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A body of mas...

Question

A body of mass 'M'is revolving in a vertical circle of radius 'R' what is the difference in the kinetic energies at the bottom and top portion of the circle?

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Solution

K.E. at bottom point = $K E_{1} = \frac{1}{2} m v_{1}^{2}$
P.E. at bottom point = $P E_{1} = 0$
K.E. at top point = $K E_{2} = \frac{1}{2} m v_{1}^{2}$
P.E. at top point = $P E_{2} = m g h$
$K E_{1} + P E_{1} = K E_{2} + P E_{2} . . . . . .$ [ conservation of energy]
$\frac{1}{2} m v_{1}^{2} + 0 = \frac{1}{2} m s_{2}^{2} + 2 m g R$
$K E_{1} - K E_{2} = 2 m g R$

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