The masses of the Earth and the Moon are and respectively

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

The masses of the Earth and the Moon are

5.97\times10^{24}\,\text{kg}

and

7.35\times10^{22}\,\text{kg}

respectively. The distance between their centres is

3.84\times10^{8}\,\text{m}

. (a) Let a point

P

lie on the straight line joining the centres of the Earth and the Moon, at a distance

x

from the centre of the Moon. Derive an expression for

x

for which the net gravitational force on a unit mass placed at

P

is zero. (b) Calculate the numerical value of

x

. (c) Is point

P

closer to the Earth or to the Moon? Give a brief qualitative explanation based on your result in part (b).