Correct Answer - Option 1 : v
CONCEPT:
-
Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.
P = mv
where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.
-
Momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.
-
Kinetic energy: The energy in a body due to its motion, is known as kinetic energy.
The kinetic energy in terms of momentum is given by:
\(K=\frac{P^2}{2M}\)
where K is the kinetic energy of the body, P is the momentum of the body and M is the mass of the body.
CALCULATION:
Given that initially at rest vi = 0;
total mass = 4m
one fragment mas = m
mass of another fragment = 4m - m = 3m
- Since there is no external force involved so the momentum of the whole system will be conserved.
- According to the law of conservation of momentum,
- The initial momentum of the system is zero (as there is no motion initial). So the final momentum of the system will also be zero.
- This implies that the momentum of the divided parts of the particle must move in opposition to each other.
Pinitial = Pfinal
\(M_{total}V_{i} = m_1v_1 + m_2v_2\)
\(4m \times 0 = m \times 3v + 3m\times v_2\)
\(0 = m \times 3v + 3m\times v_2\)
v2 = -v
- So the second particle will move will speed v in the opposite direction of the first particle.
- Hence the correct answer is option 1.
