Question

There are two planets. The ratio of radius of the two planets is $K_r$ but ratio of acceleration due to gravity of both planets is $K_g$. What will be the ratio of their escape velocity?

• A. $(K_r{K}_g{)}^{1/2}$
• B. $(K_r{K}_g{)}^{-1/2}$
• C. $(K_r{K}_g{)}^2$
• D. $(K_r{K}_g{)}^{-2}$

Answer 1

The correct option is A $(K_r{K}_g{)}^{1/2}$

The escape velocity is the minimum velocity required to leave a planet or moon. For a rocket or other object to leave a planet, it must overcome the pull of gravity.

escape velocity =$V_e=\sqrt{\frac{2GM}{R}}$

G= universal gravitational constant

M= mass of the planet or moon

R= radius of the planet or moon

also acceleration due to gravity is given by $\frac{GM}{R^2}$

we can express escape velocity in the form of acceleration due to gravity and radius as

$V_e=\sqrt{gr}$

so ratio of escape velocity of two planet is equal to the ration of $\sqrt{gr}=\sqrt{K_r.K_g}$.

so best possible answer is option A.