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  4. Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulsive force gives a velocity of 14 m s- 1 to the heavier block in the direction of the lighter block. The velocity of the centre of mass of the system at that very moment is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-nzehu7nmdpu8.png />

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Q. Two blocks of masses $10 \, kg$ and $4 \, kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulsive force gives a velocity of $14 \, m \, s^{- 1}$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass of the system at that very moment is

Question

NTA AbhyasNTA Abhyas 2020

Solution:

At the time of applying the impulsive force block of 10 kg pushes the spring forward but 4 kg mass is at rest.
Hence,
$v_{C M}=\frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}}=\frac{10 \times 14 + 4 \times 0}{10 + 4}=\frac{140}{14}=10 \, m \, s^{- 1}$