Consider two solid spheres of radii R _ 1 = 1m , R _ 2 = 2m and...

Consider two solid spheres of radii ${R}_{1} = 1m$ , ${R}_{2} = 2m$ and masses ${M}_{1}$ and ${M}_{2},$ respectively. The gravitational field due to sphere \left(1\right) $and \left(2\right)$ are shown. The value of $\dfrac{{M}_{1}}{{M}_{2}}$ is:

Consider two solid spheres of radii R _ 1 = 1m , R _ 2 = 2m and masses M _ 1 and M _ 2 , respectively. The

Options

A $\dfrac{2}{3}$
B $\dfrac{1}{6}$
C $\dfrac{1}{2}$
D $\dfrac{1}{3}$

Correct answer

B. $\dfrac{1}{6}$

Step-by-step solution

Consider two solid spheres of radii R _ 1 = 1m , R _ 2 = 2m and masses M _ 1 and M _ 2 , respectively. The

$3 = \dfrac{G{M}_{2}}{{2}^{2}}$
$2 = \dfrac{G{M}_{1}}{{1}^{2}}$
$∴ \dfrac{3}{2} = \dfrac{1}{4}\dfrac{{M}_{2}}{{M}_{1}}$
$\dfrac{{M}_{1}}{{M}_{2}} = \dfrac{1}{6}$

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