0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

# A test particle is moving in a circular orbit in the gravitational field produced by a mass density $$\rho(r)=\dfrac{K}{r^2}$$. Identify the correct relation between the radius R of the particle's orbit and its period T.

A
$$T^2/R^3$$ is a constant
B
$$T/R$$ is a constant
C
$$T/R^2$$ is a constant
D
$$TR$$ is a constant
Solution
Verified by Toppr

#### Correct option is D. $$T/R$$ is a constant$$m=\int^R_0\rho4\pi r^2dr$$$$m=4\pi kR$$$$v\propto \sqrt {4\pi k}$$$$\dfrac{T}{R}=\dfrac{2\pi}{\sqrt{4\pi k}}$$s0 $$\dfrac{T}{R}$$ is a constant.

11
Similar Questions
Q1
A test particle is moving in circular orbit in the gravitational field produced by a mass density ρ(r)=Kr2. Identify the correct relation between the radius R of the particle's orbit and its period T-

View Solution
Q2
A test particle is moving in a circular orbit in the gravitational field produced by a mass densityρ(r)=Kr2 .Identify the correct relation between the radius R of the particle's orbit and its period T
View Solution
Q3
30.A particle of charge -q and mass m moves in a circular orbit of radius r about a fixed charge +Q.The relation between the radius of the orbit r and time period T is
View Solution
Q4
Consider a spherical gaseous cloud of mass density $$\rho (r)$$ in a free space where r is the radial distance from its centre. The gaseous cloud is made of particles of equal mass m moving in circular orbits about their common centre with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If $$\rho (r)$$ is constant in time. The particle number density $$n(r)=\rho(r)/m$$ is? (G$$=$$ universal gravitational constant)
View Solution
Q5
A particle of mass m moves in a circular orbit under the central potential field, U(r)=cr, where c is positive constant. The correct radius(r)-velocity(v) graph of the particle's motion is :
View Solution