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`

Explanation

Before explosion linear momentum was zero, as there is no external impulse on the system so linear momentum should be zero just after explosion.
` vecP_(1) + vecP_(2) +vecP_(3) = 0`
` implies 1 xx 12 hati + 2 xx 8 hatj + vecP_(3) = 0`
` vecP_(3) = - (12 hati + 16 hatj)`
`P_(3) = sqrt(12^(2) + 16^(2)) = 20 kg ms^(-1)`
`m_(3) = (P_(3))/(v_(3)) = 5 kg`