1. Tardigrade
  2. Question
  3. Physics
  4. The mass of the moon is (1/81) of the earth but its gravitational pull is (1/6) of the earth. It is due to the fact that

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The mass of the moon is $ \frac{1}{81} $ of the earth but its gravitational pull is $ \frac{1}{6} $ of the earth. It is due to the fact that

Rajasthan PMTRajasthan PMT 2010

Solution:

Gravitational pull depends upon the acceleration due to gravity on that planet. $ {{M}_{m}}=\frac{1}{81}{{M}_{e}},\,\,{{g}_{m}}=\frac{1}{6}{{g}_{e}} $ $ g=\frac{GM}{{{R}^{2}}}\Rightarrow \frac{{{R}_{e}}}{{{R}_{m}}}={{\left( \frac{{{M}_{e}}}{{{M}_{m}}}\times \frac{{{g}_{m}}}{{{g}_{e}}} \right)}^{1/2}} $ $ ={{\left( 81\times \frac{1}{6} \right)}^{1/2}} $ $ \therefore $ $ {{R}_{e}}=\frac{9}{\sqrt{6}}{{R}_{m}} $