Question

The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio:

• A. 1 : 2
• B. 2 : 1
• C. 3 : 5
• D. 5 : 3

Answer 1

The correct option is B 2 : 1

Acceleration due to gravity on earth is given by
$g=\frac{G{M}_e}{R_e^2}$

or $g\propto \frac{M_e}{R_e^2}$

Hence, $\frac{g_{P_1}}{g_{P_2}}=\frac{M_{P_1}}{M_{P_2}}\times {\left(\frac{R_{P_2}}{R_{P_1}}\right)}^2$ ...(i)

Given, $\frac{M_{P_1}}{M_{P_2}}=\frac{1}{2}$ and $\frac{R_{P_2}}{R_{P_1}}=\frac{1}{2}$
Substituting the given value in Eq. (i), we get
$\frac{g_{P_1}}{g_{P_2}}=\frac{1}{2}\times {\left(\frac{2}{1}\right)}^2=\frac{2}{1}$
$\therefore g_{P_1}:g_{P_2}=2:1$