A body when fully immersed in a liquid of specific gravity 1.2 weighs 44gwt. The same body when fully immersed in water weighs 50 gwt. The mass of the body is A. 36g B. 48g C. 64g D. 80g

To solve this problem, we need to apply the principle of buoyancy, which helps us understand how objects behave when they are submerged in fluids. The weights given are in "gwt," which stands for grams weight, a unit that reflects the force of gravity acting on the mass. Let's break down the information provided and find the mass of the body step by step.

Understanding Buoyancy

When an object is immersed in a fluid, it experiences an upward force known as buoyancy. This force is equal to the weight of the fluid displaced by the object. The weight of the object in air is different from its weight in the fluid due to this buoyant force.

Given Data

• Weight of the body in a liquid with specific gravity 1.2: 44 gwt
• Weight of the body in water: 50 gwt

Calculating the Buoyant Force

First, we can determine the buoyant force when the body is immersed in both the liquid and water. The difference in weight provides us with information about the volume of the body and the density of the fluids.

1. Buoyant Force in Water

When the body is submerged in water, the buoyant force can be calculated as:

Buoyant Force in Water = Weight in Air - Weight in Water

Buoyant Force in Water = 50 gwt - Weight of body in water

2. Buoyant Force in Liquid

Using the same concept for the liquid with specific gravity 1.2, we calculate:

Buoyant Force in Liquid = Weight in Air - Weight in Liquid

Buoyant Force in Liquid = 44 gwt - Weight of body in the liquid

Relationship Between Specific Gravity and Density

The specific gravity of the liquid is 1.2, which means its density is 1.2 times that of water. Since the density of water is approximately 1 g/cm³, the density of the liquid is:

Density of Liquid = 1.2 g/cm³

Establishing Equations

Let the mass of the body be denoted by 'm'. The weight in air is given as:

Weight in Air = m * g (where g is the acceleration due to gravity)

Now, from the buoyancy principles:

• Buoyant Force in Water = m - 50 gwt
• Buoyant Force in Liquid = m - 44 gwt

Volume Calculations

Since the buoyant force is equal to the weight of the fluid displaced, we can equate the buoyant forces to the densities and volumes:

Volume of body = m / density of body

Using the specific gravity to find the volume displaced:

• Volume in Water = (Weight in Air - 50 gwt) / 1 g/cm³
• Volume in Liquid = (Weight in Air - 44 gwt) / 1.2 g/cm³

Setting the Volumes Equal

Since the volume of the body remains constant, we set the two expressions for volume equal to each other:

(m - 50) / 1 = (m - 44) / 1.2

Solving the Equation

Cross-multiplying gives:

1.2 * (m - 50) = (m - 44)

1.2m - 60 = m - 44

0.2m = 16

m = 80 grams

Final Answer

The mass of the body is 80 grams, which corresponds to option D. This exercise illustrates how the principles of buoyancy and specific gravity work together to provide insights into the physical properties of submerged objects. If you have further questions or need clarification on any of these steps, feel free to ask!