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. 2R
• B. 4R
• C. 6R
• D. 8R

Answer 1

The correct option is C

6R

Point of zero intensity $x=\frac{\sqrt{m_1}d}{\sqrt{m_1+\sqrt{m_2}}}$

Mass of the earth $m_1=M$, Mass of the moon $m_2=\frac{M}{81}$ and distance between earth & moon d=60R
Point of zero intensity from the Earth $x=\frac{\sqrt{M\times 60R}}{\sqrt{M+\sqrt{\frac{M}{81}}}}=\frac{9}{10}\times 60R=54R$

Therefore, distance from the moon = 6R