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. 3 kg
B. 5 kg
C. 7 kg
D. 17 kg

Answer

B

Explanation

Using law of conservation of linear momentum
`vecP_(1)+vecP_(2)+vecP_(3)=0`
`m_(1)vecv_(1)+m_(2)vecv_(2)+m_(3)vecv_(3)=0`
`|m_(3)vecv_(3)|=|-(m_(1)vecv_(1)+m_(2)vecv_(2))| " " vecv_(1)botvecv_(2)`
`m_(3)v_(3)=sqrt(m_(1)^(2)v_(1)^(2)+m_(2)^(2)v_(2)^(2))`
`m_(3)4=sqrt(1^(2)xx12^(2)+2^(2)xx8^(2))`
`m_(3)4=20`
`m_(3)=(20)/(4)=5kg`