question_answer

The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero-

A) \[\frac{D}{2}\]              

B)   \[\frac{2D}{3}\]

C) \[\frac{4D}{3}\]                        

D)   \[\frac{9D}{10}\]

Correct Answer: D

Solution :

Force will be zero on zero intensity point \[x=\frac{\sqrt{{{m}_{1}}}}{\sqrt{{{m}_{1}}}+\sqrt{{{m}_{2}}}}\,\,d=\frac{\sqrt{81M}}{\sqrt{81M}+\sqrt{M}}\,D\,\,=\,\,\frac{9}{10}\,D\]