Question

The mass of the earth is 6.00 x 1024 kg and that of the moon is $ 7.40\times {{10}^{22}}kg. $ The constant of gravitation $ G=6.67\times {{10}^{-11}}\,N-{{m}^{2}}/k{{g}^{2}}. $ The potential energy of the system is $ -7.79\times {{10}^{23}}\,J. $ The mean distance between the earth and moon is

• A. $ ~3.80\times {{10}^{8}}m $
• B. $ ~3.37\times {{10}^{6}}m $
• C. $ ~7.60\times {{10}^{4}}\text{ }m $
• D. $ ~1.90\times {{10}^{2}}\text{ }m $

Answer 1

Answer: (A)

$ U=\frac{GMm}{r} $
$ \Rightarrow $ $ 7.79\times {{10}^{28}} $
$ =\frac{6.67\times {{10}^{-11}}\times 7.4\times {{10}^{22}}\times 6\times {{10}^{24}}}{r} $
$ \Rightarrow $ $ r=3.8\times {{10}^{8}}\,m $