The distance between centres of the Moon and the Earth is D. The mass of Earth is 81 times the mass of the Moon. At what distance from the centre of Earth, the gravitational field is zero?

Question

The distance between centres of the Moon and the Earth is D. The mass of Earth is 81 times the mass of the Moon. At what distance from the centre of Earth, the gravitational field is zero? (A)  (D/2) (B)  (2D/3) (C)  (4D/3) (D)  (9D/10)

Tardigrade Admin · Accepted Answer

(81GM/x2) = (GM/(D-x)2) (9/x)= (1/(D-x)) ∴ x = (9D/10)

Q. The distance between centres of the Moon and the Earth is D. The mass of Earth is 81 times the mass of the Moon. At what distance from the centre of Earth, the gravitational field is zero?

$\frac{D}{2}$

$\frac{2 D}{3}$

$\frac{4 D}{3}$

$\frac{9 D}{10}$

$\frac{81 GM}{x ^{2}} = \frac{GM}{( D - x ) ^{2}}$
$\frac{9}{x} = \frac{1}{( D - x )}$
$∴ x = \frac{9 D}{10}$

Q. The distance between centres of the Moon and the Earth is D. The mass of Earth is 81 times the mass of the Moon. At what distance from the centre of Earth, the gravitational field is zero?

2D​

32D​

34D​

109D​

x281GM​=(D−x)2GM​ x9​=(D−x)1​ ∴x=109D​

$\frac{D}{2}$

$\frac{2 D}{3}$

$\frac{4 D}{3}$

$\frac{9 D}{10}$

$\frac{81 GM}{x ^{2}} = \frac{GM}{( D - x ) ^{2}}$
$\frac{9}{x} = \frac{1}{( D - x )}$
$∴ x = \frac{9 D}{10}$