An explosion blows a rock into three parts. Two parts go off at right angles to each other . These two are `1 kg` first part moving with a velocity of `12 ms^(-1) and 2 kg` second part moving with a velocity of `8 ms^(-1)`. If the third part flies off with a velocity of `4 ms^(-1)`. Its mass would be

Options

A. `3kg`
B. `5kg`
C. `7kg`
D. `12kg`

Answer

b

Explanation

Here, From `vec(p_(1)) + vec(p_(2)) + vec(p_(3)) = 0`
`vec(p_(3)) = - (vec(p_(1)) +vec(p_(2)))`
`|vec(p_(3))| = |vec(p_(1)) + vec(p_(2)) | =sqrt(p_(1)^(2) + p_(2)^(2))`
`sqrt((1xx12)^(2) + (2xx8)^(2)) =20`
`m_(3) = (|vecp_(3)|)/(upsilon_(3)) = (20)/(4) =5kg` .