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 :

U = - C r F = - d U d r = - C r 2 F = m v 2 r C r 2 = m v 2 r v 2 ∝ 1 r

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

PhysicsW.E.P.Conservative force & potential energyMedium2 minQB

PhysicsMediumsingle choice

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 :

Options:

Answer:

Solution:

$U = - \frac{C}{r}$

$F = - \frac{d U}{d r} = - \frac{C}{r^{2}}$

$|F| = \frac{m v^{2}}{r}$

$\frac{C}{r^{2}} = \frac{m v^{2}}{r}$

$v^{2} \propto \frac{1}{r}$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Conservative force & potential energy

⏱ 2mℹ️ Source: QB

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