The velocity of block B in a pulley block system can be determined by considering the principles of Newton's laws of motion and the concept of mechanical advantage.

Understanding the Pulley Block System:
In the given system, block A is connected to block B by a rope that runs over a pulley. The pulley is assumed to be frictionless and massless. Block A is of mass mA, while block B is of mass mB.

Applying Newton's Laws of Motion:
To determine the velocity of block B, we need to consider the forces acting on both blocks and apply Newton's laws of motion.

1. Forces on Block A:
- The weight of block A (mA * g) acts downwards.
- The tension in the rope connected to block A pulls upwards.

2. Forces on Block B:
- The weight of block B (mB * g) acts downwards.
- The tension in the rope connected to block B pulls upwards.

Equating Tensions:
Since the rope is assumed to be inextensible, the tension in the rope is the same on both sides of the pulley.

1. Tension in the Rope Connected to Block A:
The tension in the rope connected to block A can be determined by considering the forces acting on it:
- Tension = Weight of block A
- Tension = mA * g

2. Tension in the Rope Connected to Block B:
The tension in the rope connected to block B can be determined by considering the forces acting on it:
- Tension = Weight of block B
- Tension = mB * g

Applying Mechanical Advantage:
The mechanical advantage of the pulley system is equal to the ratio of the tension in the rope connected to block B to the tension in the rope connected to block A. In this case, the mechanical advantage is equal to mB/mA.

Calculating Velocity of Block B:
The velocity of block B can be determined by dividing the velocity of block A by the mechanical advantage of the pulley system.

Conclusion:
The velocity of block B in the pulley block system can be calculated by dividing the velocity of block A by the mechanical advantage, which is equal to the ratio of the masses of block B and block A. By applying Newton's laws of motion and considering the forces acting on each block, we can determine the tensions in the ropes connected to both blocks, which are equal in magnitude.