• # question_answer A block ${{M}_{1}}$ of mass $2.0\text{ }kg$ is moving on a frictionless horizontal surface with a velocity of $1.0\text{ m/s}$ towards another block ${{M}_{2}}$ of equal mass kept at rest as shown. The spring constant of the spring fixed at one end of ${{m}_{2}}$ is $100N/m$. The maximum compression of the spring is: A)  $2\,cm$                      B) $5\,cm$ C)  $10\,cm$                    D) $20\,cm$

At the time of maximum compression velocities of both the blocks will be same (say V) By conservation of linear momentum. $2\times 1=4V$ $V=0.5m/s$ By conservation of energy. $\frac{1}{2}\times 2\times {{(1)}^{2}}=\frac{1}{2}\times 4\times {{(0.5)}^{2}}+\frac{1}{2}\times 100\times {{(X)}^{2}}$                 $X=0.1m=10cm$