The hydrostatic law, also known as Pascal's law, states that the rate of increase of pressure in a vertical direction is equal to the specific weight of the fluid. Let's break down this statement and understand why the correct answer is option 'B'.

1. Hydrostatic Law:
The hydrostatic law deals with the pressure exerted by a fluid at rest. It states that the pressure at any point within a fluid is the same in all directions and increases with depth.

2. Rate of Increase of Pressure:
The hydrostatic law focuses on the rate of increase of pressure in a vertical direction. As we go deeper into a fluid, the pressure increases due to the weight of the fluid above.

3. Specific Weight of the Fluid:
The specific weight of a fluid is defined as the weight per unit volume of the fluid. It is calculated by multiplying the density of the fluid by the acceleration due to gravity. The specific weight represents the force exerted by the fluid per unit volume.

4. Relationship between Pressure and Specific Weight:
According to the hydrostatic law, the rate of increase of pressure in a vertical direction is equal to the specific weight of the fluid. This means that as we go deeper into a fluid, the pressure increases at a rate that is directly proportional to the specific weight of the fluid.

5. Other Options:
Option 'A' states that the rate of increase of pressure is equal to the density of the fluid. While density does play a role in determining the pressure of a fluid, it is not directly related to the rate of increase of pressure in a vertical direction.

Option 'C' states that the rate of increase of pressure is equal to the weight of the fluid. This is incorrect because the weight of the fluid alone does not determine the rate of increase of pressure. It is the specific weight of the fluid, which takes into account both the weight and volume, that is relevant.

Option 'D' states that none of the above options are correct. However, as explained above, option 'B' is the correct answer.

In conclusion, the hydrostatic law states that the rate of increase of pressure in a vertical direction is equal to the specific weight of the fluid. This relationship helps us understand how pressure changes with depth in a fluid.