Question

A block of mass $M$ moves with a velocity $v$ along a frictionless horizontal surface towards another block of mass $2M$ at rest. The velocity of the center of mass of the system of blocks is

• A. $\frac{v}{2}$
• B. $2v$
• C. $3v$
• D. $\frac{v}{3}$
• E. $\frac{v}{4}$

Hint:

The center of mass velocity is the weighted average of the velocities of individual masses.

Answer 1

The Correct Option is D

Step 1: The velocity of the center of mass is given by: \[ V_{{cm}} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \] where $m_1 = M$, $v_1 = v$, $m_2 = 2M$, and $v_2 = 0$. 
Step 2: Substituting the values: \[ V_{{cm}} = \frac{M v + 2M \times 0}{M + 2M} \] \[ V_{{cm}} = \frac{M v}{3M} = \frac{v}{3} \] 
Step 3: Therefore, the correct answer is (D).