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 m s^(-1) and 2 kg` second part moving with a velocity `8 m s^(-1)`. If the third part flies off with a velocity of `4 m s^(-1), its mass would be

Options

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

Answer

D

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 hte direction opposite to hte resultant of these two momenta.
`:. ` Momentum of the third piece = `20 kg m s^(-1)`
velocity = `4 ms^(-1)`
`:. ` Mass of the `3^(rd)` piece =`(mv)/v = 20/4 = 5 kg. `