An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 `ms^(-1)` and the second part of mass 2 kg moves with 8 `ms^(-1)` speed. If the third part flies off with 4 `ms^(-1)` speed, then its mass i s .....

Options

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

Answer

C

Explanation

Suppose mass of rock is M and velocity `vec( V ) = 0 ` mass of first piece `m_(1) = 1` kg and velocity `vec( v) _(1) = 12 hat(I ) m//s`
Mass of thir piece `m_(3) =?` and magnitude of velocity `v_(3) =4 m//s`
From the law of conservation of momentum
Momentum of rock = addition of momentum
Magnitude `m_(3) v_(3) = sqrt((12)^(2) + (16)^(2))`
`=sqrt(144+256)`
`=sqrt(400) =20 kgms^(-1)`
`m_(3) = (20)/(v_(3) ) = (20)/(4) =5 kg`