Question

If two objects of mass $m_1 = 80$g and $m_2 = 120$g moves with same speed 6cm/s, find the velocity of centre of mass

Hint:

Always pay attention to the vector nature of velocity. "Speed" is a scalar magnitude. If direction isn't specified in a two-body problem, consider opposite directions as it's the more physically interesting case often tested.

Answer 1

Step 1: Formula for Centre of Mass Velocity
\[ v_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

Step 2: Assume Directions
Since only speed is given, assume opposite directions:
\[ v_1 = +6 \text{ cm/s}, \quad v_2 = -6 \text{ cm/s} \]

Step 3: Substitute Values
\[ v_{cm} = \frac{(80)(6) + (120)(-6)}{80 + 120} \]

Step 4: Simplify
\[ v_{cm} = \frac{480 - 720}{200} \] \[ v_{cm} = \frac{-240}{200} = -1.2 \text{ cm/s} \]

Step 5: Interpret Result
Negative sign indicates motion towards heavier mass (120 g).

Step 6: Final Answer
\[ \boxed{v_{cm} = 1.2 \text{ cm/s}} \]