Question

Mass of moon is $7.34\times {10}^{22}kg$. If the acceleration due to gravity on the moon is $1.4m{s}^{-2}$, the radius of the moon is $[G=6.667\times {10}^{-11}N{m}^{2}k{g}^{-2}]$

• A. $0.56\times {10}^{4}m$
• B. $1.87\times {10}^{6}m$
• C. $1.92\times {10}^{6}m$
• D. $1.01\times {10}^{6}m$

Answer 1

The correct option is B $1.87\times {10}^{6}m$

Acceleration due to gravity on the moon's surface is $g_m=\frac{G{M}_m}{R_m^2}$

or $R_m=\sqrt{\frac{GM}{g_m}}=\sqrt{\frac{(6.67\times {10}^{-11})(7.34\times {10}^{22})}{1.4}}=1.87\times {10}^{6}m$