question_answer

If the mass of the earth is 80 times that of moon and its radius is two times that of the moon, and g on the earth is \[9.8\,m/{{s}^{2}}\], then value of g on the moon will be :

A)  \[4.9\,m/{{s}^{2}}\]       

B)  \[0.49\,m/{{s}^{2}}\]

C)  \[0.98\,m/{{s}^{2}}\]      

D)  \[9.8\,m/{{s}^{2}}\]

Correct Answer: B

Solution :

From law of gravitation the force of attraction acting on moon due to earth is \[F=G\frac{{{M}_{e}}m}{R_{e}^{2}}\] ... (i) where G is gravitational constant and Mg is mass of earth. From Newtons second law, \[F=mg\] ? (ii) From Eqs. (i) and (ii), we get \[g=\frac{G{{M}_{e}}}{{{R}_{e}}^{2}}\] \[\Rightarrow \] \[\frac{{{g}_{e}}}{{{g}_{m}}}=\frac{{{M}_{e}}}{{{M}_{m}}}{{\left( \frac{{{R}_{m}}}{{{R}_{e}}} \right)}^{2}}\] Given, \[{{M}_{e}}=80\,{{M}_{m}},\,\,{{R}_{e}}=2\,{{R}_{m}}\] \[\therefore \] \[\frac{{{g}_{e}}}{{{g}_{m}}}=\frac{80\,\,{{M}_{m}}}{{{M}_{m}}}{{\left( \frac{{{R}_{m}}}{2{{R}_{m}}} \right)}^{2}}\] \[=80\times \frac{1}{4}=20\] \[\Rightarrow \] \[{{g}_{m}}=\frac{{{g}_{e}}}{20}=\frac{9.8}{20}=0.49\,m/{{s}^{2}}\]