A bomb at rest explodes into three parts of the same mass. The linear momentum of two parts are `-2phat(i)` and `p hat(j)`. The magnitude of momentum of third part is `psqrt(x)`. Find x.

Options

A. p
B. `sqrt(5)p`
C. `2 p`
D. `10 p`

Answer

B

Explanation

Given, `p_(1)=2phat(i)=2p` along negative x-axis.
`p_(2)=phat(i)=p` along y-axis.
The resultant momentum of two parts
`p'=sqrt(p_(1)^(2)+p_(2)^(2))=sqrt((2p)^(2)+p^(2))=psqrt(5)`
As the bomb was initially at rest final momentum of all the three parts must be zero
`p_(3)+p'=0`
`p_(3)=-p'=-psqrt(5)=sqrt(5)p`
`p_(3)=sqrt(5)p`