A conducting sphere of radius $R$ carrying charge $Q$ , lies concentrically inside an uncharged conducting shell of radius $2 R$ . When joined by a metal wire

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$\frac{Q}{3}$ amount of charge will flow from the sphere to the shell

$\frac{2 Q}{3}$ amount of charge will flow from the sphere to the shell

$Q$ amount of charge will flow from the sphere to the shell

$\frac{Q^{2}}{16 {πε}_{0} R}$ amount of heat will be produced

answer is C, D.

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Detailed Solution

On connecting the conducting sphere having charge $Q$ with a conducting shell having no charge, the entire charge must flow out to the uncharged shell. Option $(3)$

The capacitance of the outer shell of radius $2 R$ is $C' = 4 {πε}_{0} (2 R)$
So energy liberated is $U = \frac{Q^{2}}{2 C} = \frac{Q^{2}}{16 π ε_{0} R}$