Question

Knowing that mass of Moon is $\frac { M } { 81 }$ where M is the mass of Earth, find the distance of the point where gravitational field due to Earth and Moon cancel each other, from the Moon. Given that distance between Earth and Moon is 60 R. Where R is the radius of Earth

• A. 2 R
• B. 4 R
• C. 6 R
• D. 8R

Answer 1

Answer: (C)

6 R

Answer 2

Point of zero intensity $x = \frac { \sqrt { m _ { 1 } } d } { \sqrt { m _ { 1 } } + \sqrt { m _ { 2 } } }$

mass of the earth m₁ $= M$ , Mass of the moon m₂ $= \frac { M } { 81 }$

and distance between earth & moon d

Point of zero intensity from the Earth

$x = \frac { \sqrt { M } \times 60 R } { \sqrt { M } + \sqrt { \frac { M } { 81 } } } = \frac { 9 } { 10 } \times 60 R = 54 R$

So distance from the moon $= 60 R - 54 R = 6 R$

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