Question

# A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity $$30$$ meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be

A
102 m/second and 135o from either
B
102 m/second and 45o from either
C
102 m/second and 135o from either
D
102 m/second and 45o from either

Solution

## The correct option is B $$10 \sqrt{2}$$ m/second and $$135^o$$ from eitherLet two pieces are having equal mass m and third piece have a mass of $$3 m$$ According to law of conservation of linear momentum. Since  the initial momentum of the system was zero, therefore final momentum of the system must be zero i.e. the resultant of  momentum of two pieces must be equal to the momentum of third piece. We know that if two particle possesses same  momentum and angle in between them is $$90^0$$ then resultant will be given by $$P \sqrt {2} = mv \sqrt {2} = m 30 \sqrt {2}$$$$\therefore V = 10 \sqrt {2}$$ and angle $$135^0$$ from either.Physics

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