# 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

#### 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.