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Physics - W.E.P. Question with Solution | TestHub

PhysicsW.E.P.MiscellaneousMedium2 minQB

PhysicsMediumsingle choice

Two particles of the same mass $m$ are moving in circular orbits because of force, given by $F (r) = - \frac{16}{r} - r^{3}$ . 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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Answer:

Solution:

Centripetal force is given as $F (r) = \frac{m v^{2}}{r}$ .

Given in the problem, $\frac{m V^{2}}{r} = \frac{16}{r} + r^{3} . . . (i)$

Kinetic energy is stated as $K E_{0} = \frac{1}{2} m v^{2}$ .

$K E_{0} = \frac{1}{2} [16 + r^{4}]$ (From equation $(i)$ )

The ratio of kinetic energies of first and second particle is $\frac{K_{1}}{K_{2}} = \frac{\frac{16 + 1}{2}}{\frac{16 + 256}{2}} = \frac{17}{272}$

$\frac{K_{1}}{K_{2}} ≃ 6 \times 10^{- 2}$ .

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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