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

Answer

`(1)`

Explanation

When an explosion breaks a rock , by the law of conservation of momentum, initial momentum is zero and for the three pieces, Total momentum of the two pieces 1 kg and 2 kg = `sqrt((12)^(2) + 16^(2)) = 20 kg ms^(-1)`.
The third piece has the same momentum and in the direction opposite to the resultant of these two momenta. `therefore` Momentum of the third piece = `20 kg ms^(-1)`
`"Velocity" = 4ms^(-1)`
`therefore "Mass of the 3rd piece" = 20/4 = 5 kg`