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 v_{i} = 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
\(M_{total}V_{i} = m_1v_1 + m_2v_2\)
\(4m \times 0 = m \times 3v + 3m\times v_2\)
\(0 = m \times 3v + 3m\times v_2\)
v_{2} = 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.