Question

Mass of moon is $\frac{1}{80}th$of that of earth and its radius is $\frac{1}{4}th$of radius of earth. Acceleration due to gravity on the surface of moon as compared with that on the surface of earth is:

• A. $2$
• B. $\frac{1}{2}$
• C. $\frac{1}{5}$
• D. $5$

Answer 1

The correct option is C

$\frac{1}{5}$

Step 1: Given

$$\begin{gathered} M_{moon}=\frac{1}{80}\times M_{earth} \\ {R}_{moon}=\frac{1}{4}\times R_{earth} \\ \frac{g_{moon}}{g_{earth}}=? \end{gathered}$$

Step 2: Writing the expressions for acceleration due to gravity on earth and moon

$$\begin{gathered} g_{earth}=G\frac{M_{earth}}{{R_{earth}}^2} \\ {g}_{moon}=G\frac{M_{moon}}{{R_{moon}}^2} \end{gathered}$$

Step 3: Replacing the value of Moon's mass and radius in terms of the earth's mass and radius

$$\begin{gathered} g_{moon}=G\frac{\frac{1}{80}\times M_{earth}}{{\left(\frac{1}{4}\times R_{earth}\right)}^2} \\ =\frac{1}{5}\times G\frac{M_{earth}}{{R_{earth}}^2} \\ =\frac{1}{5}\times g_{earth} \\ \Rightarrow \frac{g_{moon}}{g_{earth}}=\frac{1}{5} \end{gathered}$$

Hence, the correct answer is option (C).