# Two identical blocks P and Q each of mass 2 kg are placed on a smooth horizontal surface as shown. Block Q is connected a light spring of force constant 100 N/m.If block 'p' is given an initial velocity 4 m/s towards the block 'Q' the maximum compression in the spring will be:

Max compression will occur when both has same velocity and equal to half of initial velocity

$\begin{array}{l} \Rightarrow \frac{1}{2} l x^{2}=\frac{1}{2} m(4)^{2}-\frac{1}{2} m(2)^{2} \times 2 \\ \Rightarrow k x^{2}=16 m-8 m \\ \Rightarrow k x^{2}=8 m \\ \Rightarrow x^{2} \frac{8 m}{k}=\frac{8 \times 2}{100} \\ \Rightarrow x=\frac{4}{10}=0.4 m \end{array}$

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