The objects at rest suddenly explodes into three parts with the mass ratio 2:1:1. The parts of equal masses moves at right angles to each other with equal speeds. The speed of the third part after the explosion will be

Options

A. 2v
B. `v/sqrt2`
C. `v/2`
D. `sqrt2v`

Answer

B

Explanation

Resultant momentum of two part of equal mass
`p_(1)=sqrt((mv)^(2)+(mv)^(2))=sqrt2mv`
ut `v^1 `= speed of third part of mass 2 m
Acc. to Law of conservation of momentum
`(2 cancel(m)) v^(1)=sqrt2 cancel(m) v`
`v^(1)=(sqrt2v)/(2)=v/sqrt2`.