Question

The figure shows two blocks of masses $6\text{kg}$ and $4\text{kg}$ placed on a frictionless surface and connected with spring. An external kick gives a velocity $15\text{m/s}$ to $6\text{kg}$ block and $10\text{m/s}$ to $4\text{kg}$ block in the opposite direction as shown. Find the velocity gain by the centre of mass of the system.

• A. $5\text{m/s}$
• B. $13\text{m/s}$
• C. $12.5\text{m/s}$
• D. $7.5\text{m/s}$

Answer 1

The correct option is A $5\text{m/s}$

We know,
$v_{com}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}$
Here
$m_1=6\text{kg},m_2=4\text{kg}$
$v_1=15\text{m/s},v_2=-10\text{m/s}$
$v_{com}=\frac{15\times 6-4\times 10}{6+4}$
$=\frac{90-40}{10}$
$V_{com}=5\text{m/s}$