A particle of mass m moves in a circular orbit under the central potential field, U(r) = -C/r, where C is a positive constant. The correct radius - velocity graph of the particle's motion is: (a) (b) (c) (d)

Answer: (b). Force F = -dU/dr = -C/r² (attractive), magnitude C/r². mv²/r = C/r² ⇒ v² = C/mr r ∝ 1/v²: r falls steeply as v rises, a decreasing curve approaching both axes. So the answer is (b).

A particle of mass m moves in a circular orbit under the central… | JEE Main 2021 (18 Mar, Shift 2)

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Centripetal Acceleration & Force

A particle of mass m moves in a circular orbit under the central potential field, $U(r) = -\frac{C}{r}$ , where C is a positive constant. The correct radius $-$ velocity graph of the particle's motion is:

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Answer: (b)

Force $F = -\frac{dU}{dr} = -\frac{C}{r^2}$ (attractive), magnitude $\frac{C}{r^2}$ .
$\frac{mv^2}{r} = \frac{C}{r^2} \Rightarrow v^2 = \frac{C}{mr}$
$r \propto \frac{1}{v^2}$ : $r$ falls steeply as $v$ rises, a decreasing curve approaching both axes.
So the answer is (b).

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