Two planets A and B travel counter clockwise is circular orbits around a fixed star. The radii of their orbits are in the ratio `1 : 4`. At some time, they are aligned as shown in the figure, making a straight line with the star. After a certain time, planet A comes back to its initial positio completing one full circle about the star in the same time, angular displacement of the planet B is :

Options

A. `22.5^(@)`
B. `45^(@)`
C. `180^(@)`
D. `360^(@)`

Answer

B

Explanation

`T^(2) xx r^(3)`
So `(T_(A))/(T_(B))=((r_(A))/(r_(B)))^(3//2)=(1)/(8)`
As angular displacement of A is `360^(@)`, angular displacement of B will be `(360^(@))/(8) = 45^(@)`