**Finding the Relative Density**

The relative density of a material can be determined by comparing its weight in air with its weight in water. Here, we are given the weight of a body in air and in water, and we need to find the relative density of the material.

To find the relative density, we can use the principle of buoyancy. When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force reduces the weight of the object when it is in water compared to when it is in air.

**Weight in Air**

The weight of the body in air is given as (5.00 - 0.05) N. The value is given as a range, which indicates the uncertainty in the measurement. The average weight in air is 5.00 N, and the uncertainty is ±0.05 N.

**Weight in Water**

The weight of the body in water is given as (4.00 - 0.05) N. Again, the average weight in water is 4.00 N, with an uncertainty of ±0.05 N.

**Buoyant Force and Weight Difference**

The difference between the weight of the body in air and in water is due to the buoyant force acting on the body when it is submerged in water. This weight difference is equal to the buoyant force, which is given by the weight of the water displaced by the body.

We can calculate the weight difference between the body in air and in water as follows:

Weight difference = Weight in air - Weight in water
= (5.00 - 0.05) N - (4.00 - 0.05) N
= 1.00 N

**Relative Density Calculation**

The relative density of a material is defined as the ratio of its density to the density of a reference material, usually water. It can be calculated using the following formula:

Relative density = Weight difference / Weight of the displaced water

Since the weight difference is 1.00 N and the weight of the displaced water is equal to the weight in air, which is 5.00 N, the relative density can be calculated as follows:

Relative density = 1.00 N / 5.00 N
= 0.20

Therefore, the relative density of the material is 0.20.

**Maximum Percentage Error**

The maximum percentage error can be determined by considering the uncertainties in the measurements. In this case, the uncertainties in the weight in air and weight in water are both ±0.05 N.

The maximum percentage error can be calculated using the following formula:

Maximum percentage error = (Maximum uncertainty / Average value) * 100

For the weight in air:

Maximum uncertainty = ±0.05 N
Average value = 5.00 N

Maximum percentage error = (0.05 N / 5.00 N) * 100
= 1.00%

Similarly, for the weight in water:

Maximum uncertainty = ±0.05 N
Average value = 4.00 N

Maximum percentage error = (0.05 N / 4.00 N) * 100
= 1.25%

Therefore, the maximum percentage error in the relative density calculation is 1.00% for the weight in air and 1.25% for the weight in water

11%