Question

Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively :

• A. 4 m/s, 4 m/s
• B. 10 m/s, 4 m/s
• C. 4 m/s, 10 m/s
• D. 10 m/s, 10 m/s

Answer 1

The correct option is C 4 m/s, 10 m/s

Velocities of $5kg$ block and $2kg$ block are $14$ $m/s$ and zero respectively.

Let velocity of its centre of mass be $V_{CM}$

$V_{CM}=\frac{m_{1}v+m_2{v}^{\prime }}{m_1+M_2}$

$V_{CM}=\frac{5\left(14\right)+2\left(0\right)}{5+2}=10$ $m/s$

Velocity of $5kg$ block in $COM$ frame, $V=v-V_{CM}=14-10=4$ $m/s$

Velocity of $2kg$ block in $COM$ frame, $V^{\prime }=v^{\prime }-V_{CM}=0-10=-10$ $m/s$

$⟹|V^{\prime }|=10$ $m/s$