A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directio - PHYSICS MCQ NEET 2019 2026 | ExamTest.live

hardMCQNEET 20192026PHYSICS

1 mark

A particle of mass 5 m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is:

Solution & Step-by-step Explanation

Total mass = 5 m . Fragments are m, m, and 3 m .By conservation of linear momentum: p_{1} + p_{2} + p_{3} = 0 .Let p_{1} = m v \hat{i} and p_{2} = m v \hat{j} . p_{3} = - (m v \hat{i} + m v \hat{j}) .Magnitude of momentum of the third piece: ∣ p_{3} ∣ = (m v)^{2} + (m v)^{2} = 2 m v .Velocity of third piece: v_{3} = \frac{2 m v}{3 m} = \frac{2 v}{3} .Energy released = Total Kinetic Energy: K = \frac{1}{2} m v^{2} + \frac{1}{2} m v^{2} + \frac{1}{2} (3 m) (\frac{2 v}{3})^{2} K = m v^{2} + \frac{1}{2} (3 m) (\frac{2 v ^{2}}{9}) = m v^{2} + \frac{1}{3} m v^{2} = \frac{4}{3} m v^{2} .

Try it yourself before checking the explanation above.

A particle of mass 5 m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular directions with speed v each. The energy released during the process is:

\frac{2}{3} m v^{2}

\frac{5}{3} m v^{2}

\frac{3}{2} m v^{2}

\frac{4}{3} m v^{2}

Practice with timed mock tests and track your performance across PHYSICS.