Two particles of the same mass m are moving in circular orbits because of force, given by F r = - 16 r - r 3 . The first particle is at a distance r = 1 , and the second, at r = 4 . The best estimate for the ratio of kinetic energies of the

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Two particles of the same mass m are moving in circular orbits because of force, given by F r = - 16 r - r 3 . The first particle is at a distance r = 1 , and the second, at r = 4 . The best estimate for the ratio of kinetic energies of the first and the second particle is closest to

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Correct answer: C. 6 × 10 - 2

Centripetal force is given as F r = m v 2 r . Given in the problem, m V 2 r = 16 r + r 3 &#160; &#160; . . . i Kinetic energy is stated as K E 0 = 1 2 m v 2 . K E 0 = 1 2 16 + r 4 (From equation i ) The ratio of kinetic energies of first and second particle is K 1 K 2 = 16 + 1 2 16 + 256 2 = 17 272 K 1 K 2 &#160; &#8771; 6 &#160; &#215; 10 - 2 .

Two particles of the same mass m are moving in circular orbits because of force, given by F r = - 16 r - r 3 . The first particle is at a distance r = 1 , and the second, at r = 4 . The best estimate for the ratio of kinetic energies of the first and the second particle is closest to

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