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

Here, initial momentum is zero. According to law of conservation of linear momentum,
Initial momentum`=` final momentum
`vec(p_(1))+vec(p_(2))+vec(p_(3))=1xx12 hat(i)+2xx8hat(j)+vec(p_(3))=0`
or `vec(p_(3))=(12hat(i)+16 hat(j))`
`:. p_(3)=sqrt((12)^(2)+(16)^(2))=20kg m//s`
`m_(3)=(p_(3))/(upsilon_(3))=(20)/(4)=5kg`