Question

Two planets have average radii of their orbits of revolution in the ratio 64:9. Then the ratio of their period of revolution is:

• A. 12:69
• B. 3:4
• C. 512 : 27
• D. 27:512

Answer 1

The correct option is C 512 : 27

We know that square of the orbital speed of the orbit of a planet is directly proportional to the cube of radius of revolution.

$T^2\propto (r{)}^3$

$\Rightarrow T_1$ : $T_2$ = ${64}^{\frac{3}{2}}:9^{\frac{3}{2}}$

So, period of revolution = $8^3:3^3=512:27$