Question

The gravitational pull of the moon is $(\frac{1}{6})^{th}$ of the earth and mass of moon is $(\frac{1}{8})^{th}$ of the earth. This implies that the

• A. radius of moon is $(1/4)^{th}$ of the earth's radius.
• B. radius of the earth is $(\sqrt{4/3})^{th}$ of the moon's radius.
• C. moon's radius is half that of the earth.
• D. radius of the earth is $(4/3)^{th}$ of the moon's radius.

Hint:

Gravity is directly proportional to mass and inversely proportional to the square of the radius.

Answer 1

The Correct Option is B

Step 1: Formula
$g = \frac{GM}{R^2}$
Step 2: Ratio of gravity
$\frac{g_m}{g_e} = \frac{M_m}{M_e} \times \left(\frac{R_e}{R_m}\right)^2$
Step 3: Substitution
$\frac{1}{6} = \frac{1}{8} \times \left(\frac{R_e}{R_m}\right)^2$
$\left(\frac{R_e}{R_m}\right)^2 = \frac{8}{6} = \frac{4}{3}$
Step 4: Calculation
$\frac{R_e}{R_m} = \sqrt{\frac{4}{3}}$
Final Answer:(B)