Question

A mass M moving with velocity V along X-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3V. The velocity of the combination, after the collision is

• A. \(V\hat{i}+2V\hat{j}\)
• B. \(\frac{V}{3}\hat{i}+2V\hat{j}\)
• C. \(V\hat{i}+3V\hat{j}\)
• D. \(2V\hat{i}+4V\hat{j}\)

Hint:

Conserve momentum separately along X and Y; the total mass is 3M.

Answer 1

The Correct Option is B

Step 1: Use the centre of mass velocity:
After sticking, the pair moves with the velocity of the centre of mass: $\vec v_{cm}=\dfrac{m_1\vec v_1+m_2\vec v_2}{m_1+m_2}$.

Step 2: Substitute:
$\vec v_{cm}=\dfrac{M(V\hat i)+2M(3V\hat j)}{3M}=\dfrac{V\hat i+6V\hat j}{3}$.

Step 3: Simplify:
$\vec v=\dfrac V3\hat i+2V\hat j$. Option B.

Final Answer:
Momentum is conserved along each axis with total mass 3M. \[ \boxed{\text{(B) }\dfrac V3\hat i+2V\hat j} \]