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(B) Consider the blocks in the frame of the accelerating plank. $A$ pseudo force $F_p = m \cdot a$ acts on each block in the direction opposite to the

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spring will be in its natural length under all conditions.

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(B) Consider the blocks in the frame of the accelerating plank. $A$ pseudo force $F_p = m \cdot a$ acts on each block in the direction opposite to the acceleration of the plank.For block $m_1$,the forces acting are the pseudo force $m_1 a$ (leftward) and the frictional force $f_1 = \mu m_1 g$ (rightward).The net acceleration of block $m_1$ relative to the plank is $a_{net,1} = a - \mu g$.Similarly,for block $m_2$,the net acceleration relative to the plank is $a_{net,2} = a - \mu g$.Since both blocks experience the same net acceleration relative to the plank,they do not move relative to each other.Therefore,the spring remains in its natural length under all conditions,and its extension $x = 0$.

Two blocks of masses $m_1$ and $m_2$ are connected with a massless unstretched spring and placed over a plank moving with an acceleration '$a$' as shown in the figure. The coefficient of friction between the blocks and the platform is $\mu$.

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