Question

Two planets A and B have radii R and R/n^2 respectively what is the ratio of the time periods of their revolution

Answer 1

According to orbital law 

$$\frac{T_A^2}{T_B^2}=\frac{R_A^3}{R_B^3}$$

$$\frac{T_A^2}{T_B^2}=\frac{n^6R^3}{R^3}=n^6$$

Thus,

$$\frac{T_A}{T_B}=n^3$$