At what distance from the centre of the moon | vedclass

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(A) Let $M_e$ be the mass of the Earth and $M_m$ be the mass of the Moon. Given $M_e = 81 M_m$.Let $x$ be the distance from the centre of the Moon whe

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let $M_e$ be the mass of the Earth and $M_m$ be the mass of the Moon. Given $M_e = 81 M_m$.Let $x$ be the distance from the centre of the Moon where the resultant gravitational field is zero.The distance from the centre of the Earth to this point is $(60R - x)$.At this point,the gravitational field intensity due to the Earth must be equal to that due to the Moon:$\frac{G M_e}{(60R - x)^2} = \frac{G M_m}{x^2}$Substituting $M_e = 81 M_m$:$\frac{81 M_m}{(60R - x)^2} = \frac{M_m}{x^2}$$\frac{81}{(60R - x)^2} = \frac{1}{x^2}$Taking the square root on both sides:$\frac{9}{60R - x} = \frac{1}{x}$$9x = 60R - x$$10x = 60R$$x = 6R$Thus,the distance from the centre of the Moon is $6\,R$.

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