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In Fig, A and B are two identical blocks made of a conducting material. These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant 'k'. Unstretched length of the spring is $L_{0}$ . A total charge Q is now given to the system. Consequently, the spring stretches to an equilibrium length L. Value of Q is :

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$L \sqrt{4 π ε_{0} K (L - L_{0})}$

$4 π ε_{0} K (L - L_{0})$

$\sqrt{4 π ε_{0} KL}$

$L \sqrt{\frac{K}{4 π ε_{0}} (L - L_{0})}$

answer is C.

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Detailed Solution

Net force on each block is zero so

$K (L - L_{0}) = \frac{Q^{2}}{4 π ε_{0} L^{2}} \Rightarrow Q = L \sqrt{4 π ε_{0} K (L - L_{0})}$

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