Question

Two bodies of masses $2~\text{kg}$ and $3~\text{kg}$ move at right angles with velocities $20~\text{m/s}$ and $10~\text{m/s}$ respectively.
Then the velocity of the centre of mass of the system is

• A. $5~\text{m/s}$
• B. $30~\text{m/s}$
• C. $10~\text{m/s}$
• D. $14~\text{m/s}$

Hint:

Use vector components and apply $V_{cm} = \dfrac{\sum mv}{\sum m}$ in each direction.

Answer 1

The Correct Option is C

Total mass $= 2 + 3 = 5~\text{kg}$
x-momentum $= 2 \cdot 20 = 40$ \quad y-momentum $= 3 \cdot 10 = 30$
$V_{cm,x} = \dfrac{40}{5} = 8$, \quad $V_{cm,y} = \dfrac{30}{5} = 6$
Magnitude: $V_{cm} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10~\text{m/s}$