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Two thin spherical shells A and B, each having radius ‘R’, are kept in contact with each other as shown in figure. Then if F be the magnitude of mutual gravitational force of attraction, then

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$F α \frac{1}{R^{2}}$

$F α \frac{1}{R^{4}}$

$F α R^{2}$

$F α R^{4}$

answer is C.

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Detailed Solution

Mass of shells are $m_{1} = 4 {πR}^{2} σ_{1} and m_{2} = 4 {πR}^{2} σ_{2}$
Where $σ_{1} and σ_{2}$ are surface density of mass of the shells .

$\begin{array}{l} m_{1} = 4 {πR}^{2} σ_{1} and m_{2} = 4 {πR}^{2} σ_{2} \\ ∴ F = G \frac{m_{1} m_{2}}{4 R^{2}} = (4 π^{2} G σ_{1} σ_{2}) R^{2} \\ ∴ F \propto R^{2} \end{array}$

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