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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 metre 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

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B

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C

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D

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Solution

## The correct option is A Let two pieces are having equal mass m and third piece have a mass of 3m. 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 possess same momentum and angle in between them is 90âˆ˜ then resultant will be given by Pâˆš2=mvâˆš2=m30âˆš2 Let the velocity of mass 3m is v. So 3mV=30mâˆš2 âˆ´V=10âˆš2 and angle 135âˆ˜ from either. (as it is clear from the figure)

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