Shell in a shell

Classical Mechanics Level pending

A spherical shell of volume mass density \(\rho\), thickness \(t\) and radius \(R\) (with \(R >> t\)) is placed concentrically inside another shell of radius \(2R\) having the same thickness and of the same material as shown in the figure.

If the circumferential stress developed in the outer shell is \(x G \pi R t \rho^2 \), find \(x\).

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