A body of mass 2 kg is moving under the influence of central force whose potential energy is given by U = 2r³ J. If the body is moving in a circular orbit of 5 m, its energy will be

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625 J

250 J

500 J

125 J

answer is A.

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Detailed Solution

$F = - \frac{du}{dr} = - 6 r^{2}$

$\frac{{mv}^{2}}{r} = 6 r^{2}$

${mv}^{2} = 6 r^{3}$

$\frac{1}{2} {mv}^{2} = 3 r^{3}$

$E = U + K = 2 r^{3} + 3 r^{3} = 5 r^{3}$

$E = 5 (5)^{3} = 5 (125) = 625 J$

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