$\begin{array}{1 1} \large\frac{1}{3} \\\large\frac{7}{3} \\ \large\frac{4}{3} \\ \large\frac{8}{3} \end{array}$

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Let $m$ be the mass of core and $m_2$ mass of outer shell

$g_A=g_B$ (given)

$\large\frac{Gm_1}{R^2}= \large\frac{G(m_1+m_2)}{(2R)^2}$

=> $4m_1=(m_1 +m_2)$

$4 \bigg[ \large\frac{4}{3} $$\pi R^3 s_1\bigg]=\large\frac{4}{3} $$\pi R^3 s_1+\large\frac{4}{3}$$[(2R)^3-R^3]s_2]$

$4s_1=s_1 +7s_2$

$\therefore \large\frac{s_1}{s_2}=\frac{7}{3}$

Hence b is the correct answer

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