Question

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

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

Answer 1

The correct option is C

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

Initial momentum of the system

${\overrightarrow{P}}_i=mv\hat{i}+mv\hat{j}$

$|{\overrightarrow{P}}_i|$ = $\sqrt{2}mv$

Final momentum of the system = 2mV

By the law of conservation of momentum

$\sqrt{2}mv=2mV\Rightarrow V=\frac{v}{\sqrt{2}}$