The distance between earth and moon is d and the mass of earth is 81 times that of the moon. If the location of neutral point from the centre of the earth on the line joining the centres of the earth and moon is (n d/10), then find n.

Question

The distance between earth and moon is d and the mass of earth is 81 times that of the moon. If the location of neutral point from the centre of the earth on the line joining the centres of the earth and moon is (n d/10), then find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let the neutral point be located at a distance

x

from the centre of the earth on the line joining the centres of the earth and moon. If

M_{e}

and

M_{m}

are the masses of the earth and the moon, respectively, and

m

the mass of the body placed at the neutral point, then the force exerted by

M_{e}

on

m

must be equal and opposite to that of

M_{m}

on

m

.

\frac{G M _{e} m}{x ^{2}} = \frac{G M _{m} m}{( d - x ) ^{2}}

∴ \frac{M _{e}}{M _{m}} = 81 = \frac{x ^{2}}{( d - x ) ^{2}}

Since

d > x

, there is only one solution.

\frac{x}{d - x} = + 9

or

x = \frac{9}{10} d

Q. The distance between earth and moon is d and the mass of earth is 81 times that of the moon. If the location of neutral point from the centre of the earth on the line joining the centres of the earth and moon is 10nd​, then find n.

Q. The distance between earth and moon is $d$ and the mass of earth is $81$ times that of the moon. If the location of neutral point from the centre of the earth on the line joining the centres of the earth and moon is $\frac{n d}{10}$ , then find $n$ .