Understanding the concept of specific gravity is crucial in physics, especially when dealing with objects immersed in fluids. This problem involves calculating the specific gravity of an object based on its weight in air and its apparent weight when fully submerged in water.

Object Weight Data

To determine the specific gravity, we first need to identify the given weights of the object.

• Weight of the object in air (\(W_{air}\)): 60 N
• Weight of the object when fully submerged in water (\(W_{water}\)): 55 N

Specific Gravity Principle

Specific gravity is a dimensionless quantity that compares the density of an object to the density of a reference substance, typically water for liquids and solids. It can also be defined in terms of weights.

The key principle here is Archimedes' principle, which states that 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 is what causes the object to appear lighter when submerged.

The loss of weight when an object is submerged in water is equal to the buoyant force, which is also the weight of the water displaced.

Calculating Loss of Weight

The loss of weight is the difference between the object's weight in air and its weight when submerged in water. This loss of weight represents the buoyant force exerted by the water on the object.

Loss of weight = Weight in air - Weight in water

Using the given values:

$$\text{Loss of weight} = W_{air} - W_{water}$$

$$\text{Loss of weight} = 60 \text{ N} - 55 \text{ N}$$

$$\text{Loss of weight} = 5 \text{ N}$$

Specific Gravity Formula

The specific gravity (\(SG\)) of an object can be calculated using the formula that relates its weight in air to the loss of weight when submerged in water:

$$\text{Specific Gravity (SG)} = \frac{\text{Weight of object in air}}{\text{Loss of weight in water}}$$

Specific Gravity Calculation

Now, we can substitute the values we have into the specific gravity formula:

$$\text{SG} = \frac{60 \text{ N}}{5 \text{ N}}$$

$$\text{SG} = 12$$

Since specific gravity is a ratio of two weights (or densities) of the same units, it is a dimensionless quantity, meaning it has no units.

Final Specific Gravity

Based on the calculations, the specific gravity of the object is 12. This indicates that the object is 12 times denser than water.