Question

Two blocks of masses $4\text{kg}$ and $3\text{kg}$ respectively are placed on a frictionless surface and connected with a spring. Block of mass $4\text{kg}$ is given initial velocity of $7\text{m/s}$ towards the other block with the help of external force. Initial velocity of centre of mass of the system is

• A. 3 $\text{m/s}$
• B. 10 $\text{m/s}$
• C. 4 $\text{m/s}$
• D. $1\text{m/s}$

Answer 1

The correct option is C 4 $\text{m/s}$


$v_A=$ velocity of $4\text{kg}$ block
$v_B=$ velocity of $3\text{kg}$ block
As block B is connected to block A with the help of spring.
$\therefore$External force imparted to block A will not affect the block B instantaneously.
$\Rightarrow v_B=0$
We know
$v_{\text{COM}}=\frac{m_A{v}_A+m_B{v}_B}{m_A+m_B}$
$=\frac{4\times 7+3\times 0}{4+3}$
$v_{\text{COM}}=4\text{m/s}$