Question 37 of 223

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:

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

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Answer: (B) $\dfrac{1}{6}$

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