A body of mass 1000 kg is moving horizontally with velocity 6 m/s. Another body of mass 200 kg is added gently. Then what will be its new velocity?

The correct option is 5 m/s.

Step-by-Step Explanation:

To find the new velocity of the system, we can apply the law of conservation of linear momentum. Since the second body is added gently and there is no external horizontal force acting on the system, the total horizontal linear momentum of the system before and after adding the body must remain conserved.

The law of conservation of momentum states:
$p_{\text{initial}}=p_{\text{final}}$

Before the second body is added, the momentum is due only to the first body:
$p_{\text{initial}}=m_1\cdot u_1$
where:
• $m_1=1000\text{kg}$ (mass of the first body)
• $u_1=6\text{m/s}$ (initial horizontal velocity of the first body)

After the second body of mass $m_2=200\text{kg}$ is added gently (with no initial horizontal velocity of its own), the two bodies move together with a common final velocity $v$:
$p_{\text{final}}=(m_1+m_2)\cdot v$

Equating the initial and final momentum:
$m_1\cdot u_1=(m_1+m_2)\cdot v$

Substitute the given values into the equation:
$1000\cdot 6=(1000+200)\cdot v$
$6000=1200\cdot v$

Solve for the new velocity $v$:
$v=\frac{6000}{1200}$
$v=5\text{m/s}$

Thus, the new velocity of the body after the mass is added is 5 m/s.