Question

A particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northward with the same speed $v$. The two particles coalesce on collision. The new particle of mass $2m$ will move in the north-easterly direction with a velocity

• A. $v/2$
• B. $2v$
• C. $v/\sqrt{2}$
• D. $v$

Answer 1

Answer: (C)

$v/\sqrt{2}$

Answer 2

Initially both the particles are moving perpendicular to each other with momentum mv.

So the net initial momentum$= \sqrt{(mv)^{2} + (mv)^{2}} = \sqrt{2}mv$.

After the inelastic collision both the particles (system) moves with velocity V, so linear momentum = 2mV

By the law of conservation of momentum $\sqrt{2}mv = 2mV$

∴ $V = v ⥂ / ⥂ \sqrt{2}.$