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(B) By the Law of Conservation of Mechanical Energy $(COME)$,the total initial mechanical energy is equal to the total final mechanical energy.Initial

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$\sqrt{\frac{2mv^2}{k}}$

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(B) By the Law of Conservation of Mechanical Energy $(COME)$,the total initial mechanical energy is equal to the total final mechanical energy.Initial kinetic energy of the system is $KE_i = \frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$.At the point of maximum elongation $x$,the relative velocity between the two blocks becomes zero,meaning both blocks move with the same velocity (which is zero in the center of mass frame).Final potential energy of the spring is $PE_f = \frac{1}{2}kx^2$.Applying conservation of energy: $KE_i = PE_f$.$mv^2 = \frac{1}{2}kx^2$.$x^2 = \frac{2mv^2}{k}$.$x = \sqrt{\frac{2mv^2}{k}}$.

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

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