Question

A particle of mass moving eastward with a speed v collides with another particle of the same mass moving northwards with the same speed v. The two particle coalesce on collision. The new particle of mass 2m will move in the northeasterly direction with a velocity:

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

Answer 1

Answer: (C)

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

Let us apply the law of conservation of momentum to this problem. Given that the first mass moves towards east i.e., along X axis and second mass moves towards north i.e., along Y-axis.
If v and v' be the corresponding velocities, then we have mv=2mv′cosθ.