A BODY WHICH WEIGHS 50N IN AIR DISPLACES 3.7KG OF WATER WHEN PARTIALLY IMMERSED IN WATER. CALCULATE THE UPTHRUST ON THE BODY

• A. 8.7N
• B. 37.0N ✓
• C. 87.0N
• D. 13.0N

 

The answer to the question is: B. 37.0N

To calculate the upthrust on the body, we can use Archimedes’ principle, which states that the buoyant force acting on a body partially or fully immersed in a fluid is equal to the weight of the fluid displaced by the body. The formula to calculate the upthrust is given by:

Upthrust = Weight of water displaced = Volume of water displaced × Density of water × Acceleration due to gravity

First, we need to find the volume of water displaced by the body. The weight of the body in air is 50N, and it displaces 3.7kg of water when partially immersed in water.

Using the relationship between weight and mass (Weight = Mass × Acceleration due to gravity), we can convert the weight of the body from newtons to kilograms:

Weight = Mass × Acceleration due to gravity

50N = Mass × 10m/s^2

Mass = 50N / 10m/s^2

Mass = 5kg

Now, we can find the volume of water displaced using the density formula (Density = Mass / Volume):

Density of water = 3.7kg / Volume

Volume = 3.7kg / Density of water

Volume = 3.7kg / 1000kg/m^3

Volume = 0.0037m^3

Finally, we can calculate the upthrust using the formula:

Upthrust = Volume of water displaced × Density of water × Acceleration due to gravity

Upthrust = 0.0037m^3 × 1000kg/m^3 × 10m/s^2

Upthrust = 37N

Therefore, the upthrust on the body is 37.0N.