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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 v√2 North-EastConsidering X−axis along East direction, Y−axis 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′|=v√2 Now direction of motion after collision is: tanθ=v′yv′x=v2v2=1 ∴θ=45∘ ⇒Direction is North-East

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