Question

A body of mass 5 kg is moving along the x-axis with a velocity 2$m{s}^{-1}$. Another body of mass 10 kg is moving along the y-axis with a velocity $\sqrt{3}m{s}^{-1}$. If they collide at the origin and stick together, then the final velocity of the combined mass is

• A. $\sqrt{3}m{s}^{-1}$
• B. $(\sqrt{3}+1)m{s}^{-1}$
• C. $\frac{4}{3}m{s}^{-1}$
• D. $None$

Answer 1

The correct option is C $\frac{4}{3}m{s}^{-1}$

Momentum of 5 kg mass $\left(p_1\right)=5\times 2=10kgm{s}^{-1}$ along the x-axis. Momentum of 10 kg mass $\left(p_2\right)=10\sqrt{3}kgm{s}^{-1}$ along the y-axis. These two momenta are perpendicular to each other.
Therefore, the resultant initial momentum is
$P=\sqrt{p_1^2+p_2^2}=\sqrt{(10{)}^2+(10\sqrt{3}{)}^2}=20kgm{s}^{-1}$
If v $m{s}^{-1}$ is the velocity of the combined mass, then the final momentum = (10 + 5) v = 15 v kg $m{s}^{-1}$
Now, from the principle of conservation of momentum, we have 15 v = 20 or $v=\frac{4}{3}m{s}^{-1}$, which is choice (c).