# A particle of mass 4m is at rest. Suddenly it explodes into two fragments in opposite directions. If one fragment of mass m is moving with speed 3v, W

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A particle of mass 4m is at rest. Suddenly it explodes into two fragments in opposite directions. If one fragment of mass m is moving with speed 3v, What will be the speed of another fragment?
1. v
2. 2v
3. 3v
4. 4v

## 1 Answer

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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.

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