The mass of the moon is frac{M}{81},where M i | vedclass

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(C) Let $M_e = M$ be the mass of the earth and $M_m = \frac{M}{81}$ be the mass of the moon. The distance between them is $d = 60R$.Let the point wher

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(C) Let $M_e = M$ be the mass of the earth and $M_m = \frac{M}{81}$ be the mass of the moon. The distance between them is $d = 60R$.Let the point where the gravitational intensity is zero be at a distance $x$ from the center of the earth. Then the distance from the center of the moon is $(d - x)$.At this point,the gravitational field due to the earth and the moon must be equal in magnitude and opposite in direction:$\frac{GM_e}{x^2} = \frac{GM_m}{(d - x)^2}$$\frac{M}{x^2} = \frac{M/81}{(60R - x)^2}$Taking the square root on both sides:$\frac{1}{x} = \frac{1/9}{60R - x}$$60R - x = \frac{x}{9}$$9(60R - x) = x$$540R - 9x = x$$10x = 540R$$x = 54R$This is the distance from the center of the earth. The distance from the center of the moon is $d - x = 60R - 54R = 6R$.

The mass of the moon is $\frac{M}{81}$,where $M$ is the mass of the earth. The distance between the earth and the moon is $60R$,where $R$ is the radius of the earth. At what distance from the center of the moon will the gravitational intensity be zero (in $R$)?

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