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A particle of mass 1 g moving with a vel...

A particle of mass 1 g moving with a velocity `vecv_1=3hati-2hatj` `m s^(-1)` experiences a perfectly in elastic collision with another particle of mass 2 g and velocity `vecv_2=4hatj-6 hatk` `m s^(-1)`. The velocity of the particle is

A

`2.3 m s^(-1)`

B

`4.6 m s^(-1)`

C

`9.2 m s^(-1)`

D

`6 m s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
From conservation of momentum
`m_1vecv_1+m_2vecv_2=(m_1+m_2)vecv`
`1xx(3hati-2hatj)+2xx(4hatj-6hatk)=(1+2)vecv`
`implies 3hati+6hatj-12hatk=3vecv. implies vecv=hati+2hatj-4hatk`
`v=|vecv|=sqrt(1+4+16)=4.6 ms^(-1)`
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