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Question

A particle of mass m moving eastwards with a speed v collides with another particle of same mass moving northwards with same speed v. The two particles coalesces on collision. Then, the new particle of mass 2m will move with velocity:

A
v2 North-East
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B
v2 South-West
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C
v2 North-West
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D
v2 North-East
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Solution

The correct option is D v2 North-East
Considering Xaxis along East direction, Yaxis along North direction.
In this case particles are colliding obliquely, but linear momentum will be conserved since Fext=0


Initial momentum of system of particles is given as,
Pi=mv ^i+mv ^j
final momentum of system after collision,
Pf=2m×v
From P.C.L.M:
Pi=Pf
mv ^i+mv ^j=2m×v
v=v2 ^i+v2 ^j
Magnitude of the final velocity is given as:
|v|=(v2)2+(v2)2
|v|=v2
Now direction of motion after collision is:
tanθ=vyvx=v2v2=1
θ=45
Direction is North-East

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