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 $T$

Question

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

Toppr Admin · Accepted Answer

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-

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.

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.

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.

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.

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.