A body which weighs 50N in air displaces 3.7kg of water when partially immersed in water. Calculate the upthrust on the body?

1. Analyze the Question

We are given:

• Weight of the body in air ($W_{air}$) = 50 N
• Mass of water displaced ($m$) = 3.7 kg
• We need to find the Upthrust acting on the body.

2. Explain the Concept

According to Archimedes' Principle, the upthrust on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

The formula for weight is:

In physics problems for JAMB, unless otherwise specified, we use the standard value for acceleration due to gravity ($g$) as 10 m/s².

3. Show the Solution

• Step 1: Identify the mass of the displaced water. $m = 3.7\text{ kg}$
• Step 2: Calculate the weight of the displaced water using $g = 10\text{ m/s²}$. $Upthrust = m \times g$ $Upthrust = 3.7\text{ kg} \times 10\text{ m/s²}$ $Upthrust = 37.0\text{ N}$

The weight of the body in air (50 N) is extra information provided to test if you understand that upthrust depends only on the weight of the displaced fluid, not the weight of the object itself.

4. Identify the Answer

Comparing our result (37.0 N) with the given options: A. 8.7N B. 37.0N C. 87.0N D. 13.0N

The correct option is B.

5. Exam Tip

Always remember: Upthrust = Weight of displaced fluid. If the question gives you the volume of the displaced fluid instead of the mass, remember to multiply the volume by the density of the fluid to get the mass first ($m = \rho V$), then multiply by $g$. Don't get distracted by the weight of the object in air unless the question asks for the "apparent weight" (which is $W_{air} - Upthrust$).