Question

A body of mass $5kg$ is moving along the x-axis with a velocity $2m{s}^{-1}$. Another body of mass $10kg$ is moving along the y-axis with a velocity $\sqrt{3}m{s}^{-1}$. They collide at the origin and stick together. 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. $\frac{3}{4}m{s}^{-1}$

Answer 1

The correct option is C

$\frac{4}{3}m{s}^{-1}$

Momentum of 5 kg mass, $P_1=5\times 2=10kgm{s}^{-1}$ along the x-axis
Momentum of 10 kg mass, $P_2=10\sqrt{3}kgm{s}^{-1}$ along the y-axis
These two momenta are perpendicular to each other. Therefore, the resultant initial momentum is
$P_i=\sqrt{P_1^2+P_2^2}=\sqrt{(10{)}^2+(10\sqrt{3}{)}^2}=20kgm{s}^{-1}$
If $v$ is the velocity of the combined mass, then the final momentum, $P_f=(10+5)v=15v$. Now, from the principle of conservation of momentum, we have
$15v=20\Rightarrow v=\frac{4}{3}m{s}^{-1}$
Hence, the correct choice is (c).