An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1kg first part moving with a velocity of 12`ms^(-1)` and 2kg 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

We have, `p_(1) + p-(2) + p_(3) = 0` [therefore = mv]`
`therefore 1 xx12hat(i)+2xx8hat(j) + p_(3)=0`
`rArr (12hat(i) + 16hat(j) + p_(3) = 0 rArr p_(3) = -(12hat(i) + 16hat(j))`
`therefore p_(3) = sqrt(12)^(2) + (16)^(2)= sqrt(144 + 256)`
=20gk-ms^(-1)`
Now, `p_(3) = m-(3)v_(3) rArr m_(3) = (p_(3)/v_(3)) = 5kg`