Question

Mass of the Earth is $81$ times that of the moon. If the distance between the center of the Earth and the center of moon is $d$, then the distance from the center of the Earth at which the gravitational field strength due to earth - moon system is zero, is

• A. $\frac{d}{81}$
• B. $\frac{9d}{10}$
• C. $\frac{d}{10}$
• D. $\frac{8d}{9}$

Answer 1

Answer: (B)

$\frac{9d}{10}$

Let us take mass of moon to be M. Then mass of Earth will be 81M. Let the distance from the Earth be r at which gravitational field strength is zero.

Then distance from moon will be (d-r).

We calculate gravitational fields due to earth and moon at that point and equate it to zero. They will be in opposite directions.

Therefore,

$\frac{GM}{(d-r{)}^2}=\frac{G81M}{r^2}$

G and M gets cancelled

Therefore,

$9(d-r)=r$

$9d-9r=r$

$9d=10r$

$r=\frac{9d}{10}$

Option B