question_answer

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 [NCERT 1980; CPMT 1991; MP PET 1999; DPMT 1999, 2005]

A)             v/2      

B)             2v

C)             \[v/\sqrt{2}\]

D)             v

Correct Answer: C

Solution :

                Initial momentum of the system             \[{{\vec{P}}_{i}}=mv\hat{i}+mv\hat{j}\]             \[|{{\vec{P}}_{i}}|\ =\ \sqrt{2}mv\]             Final momentum of the system = 2mV             By the law of conservation of momentum             \[\sqrt{2}mv=2mV\Rightarrow V=\frac{v}{\sqrt{2}}\]