question_answer

  Radius of moon is \[1/4\] times that of earth and mass is \[1/81\] times that of earth. The point at which gravitational field due to earth becomes equal and opposite to that of moon, is (Distance between centres of earth and moon is 60R, where R is radius of earth)

A) \[5.75\text{ }R\]from centre of moon

B) 16 R from surface of moon

C) 5 3 R from centre of earth

D) 54 R from centre of earth

Correct Answer: D

Solution :

\[{{E}_{earth}}={{E}_{moon}}\]

\[\Rightarrow \,\,\,\frac{GM}{{{x}^{2}}}=\frac{GM/81}{{{(60R-x)}^{2}}}\]

\[\Rightarrow \,\,\,\,\frac{1}{x}=\frac{1}{9(60R-x)}\]

\[\Rightarrow \,\,\,x=54\,R\] from centre of earth.