QJEEM19Phe0ae: JEE Main 2019 Physics - Class 11 JEEM19Phe0ae Solution: A test particle is moving in a circular orbit in the…

Question

Verified Solution • 2025–26 Session moderate

A test particle is moving in a circular orbit in the gravitational field produced by a mass density

ρ (r) = \frac{K}{r^{2}}

. Identify the correct relation between the radius R of the particle's orbit and its period T

Accepted Answer

For circular motion of particle:

\frac{m V^{2}}{r} = m E

= m (\frac{G M}{r^{2}})

Where

M = \int_{0}^{r} (4 π x^{2} d x) (\frac{k}{x^{2}}) = 4 π k r

\Rightarrow \frac{m V^{2}}{r} = m (\frac{G (4 π k)}{r})

\Rightarrow

V = constant

T = \frac{2 π r}{V}

\Rightarrow

\frac{T}{R}

= Constant

Step-by-Step Verified Solution