Question

If the distance between centres of earth and moon is D and the mass of earth is 81 times the mass of moon, then at what distance from centre of earth the gravitational force will be zero

• A. D/2
• B. 2D/3
• C. 4D/3
• D. 9D/10

Answer 1

Answer: (D)

9D/10

Answer 2

If P is the point where net gravitational force is zero then $F _ { P A } = F _ { P B }$

$\frac { G m _ { 1 } m } { x ^ { 2 } } = \frac { G m _ { 2 } m } { ( d - x ) ^ { 2 } }$

By solving $x = \frac { \sqrt { m _ { 1 } } d } { \sqrt { m _ { 1 } } + \sqrt { m _ { 2 } } }$

For the given problem $d = D$, $m _ { 1 } =$earth, $m _ { 2 } =$ moon and $m _ { 1 } = 81 m _ { 2 }$ $\therefore m _ { 2 } = \frac { m _ { 1 } } { 81 }$

So $x = \frac { \sqrt { m _ { 1 } } D } { \sqrt { m _ { 1 } } + \sqrt { m _ { 2 } } }$ $= \frac { \sqrt { m _ { 1 } } D } { \sqrt { m _ { 1 } } + \sqrt { \frac { m _ { 1 } } { 81 } } } = \frac { D } { 1 + \frac { 1 } { 9 } } = \frac { 9 D } { 10 }$