Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision
A nucleus travelling with a velocity v emits an -particle. Let the velocities of the -particle and the residual nucleus be v ₁ and v ₂ , and let their masses be m₁ and m₂ , respectively. Which of the following statements is true?
Options
- Av ₁ + v ₂ must be parallel to v
- BNo two of the vectors v , v ₁ , and v ₂ should be parallel to each other
- Cm₁ v ₁ + m₂ v ₂ must be parallel to v
- Dv , v ₁ , and v ₂ must be parallel to one another
Correct answer
C. m₁ v ₁ + m₂ v ₂ must be parallel to v
Step-by-step solution
According to the law of conservation of linear momentum, the total momentum of the system remains conserved since no external force acts on it. Initial momentum of the nucleus = (m₁ + m₂) v Final momentum of the system after emission = m₁ v ₁ + m₂ v ₂ Equating the initial and final momentum: (m₁ + m₂) v = m₁ v ₁ + m₂ v ₂ Since (m₁ + m₂) is a positive scalar quantity, the vector m₁ v ₁ + m₂ v ₂ is a scalar multiple of v and lies in the same direction. Thus, m₁ v ₁ + m₂ v ₂ must be parallel to v .