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. 2P
D. 10p

Answer

B

Explanation

Given, `P_(1) = - 2phat(i) = 2` along negative -axis.
`P_(2) = P hat(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_(2) + P = 0`
`P_(2) = - P. = - Psqrt(5) = sqrt(5)P`
`P_(3) = sqrt(5) p`