Question

A particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northwards with the same speed. If two particles coalesce on collision, the new particle of mass $2m$ will move in the north-east direction with a velocity :

• A. $\frac{v}{2}$
• B. $v\sqrt{2}$
• C. $\frac{v}{\sqrt{2}}$
• D. None of these

Answer 1

Answer: (C)

$\frac{v}{\sqrt{2}}$

Initial momentum$=\overrightarrow{P_1}=mv\hat{i}+mv\hat{j}=mv(\hat{i}+\hat{j})$

$⟹P_1=mv\sqrt{1^2+1^2}=\sqrt{2}mv$

Final momentum $=P_2=2mV$

From Conservation of momentum-

$P_2=P_1⟹2mV=\sqrt{2}mv$

$⟹V=\frac{v}{\sqrt{2}}$

Answer-(C)