A heavy ball weighing 5 N displaces 100 ml of water when immersed in water. Calculate the apparent weight of the ball in water.

Answer

To calculate the apparent weight of the ball when it is immersed in water, we can follow these steps:

### Step 1: Understand the Problem
The weight of the ball is given as 5 N and it displaces 100 ml of water when immersed. We need to find the apparent weight of the ball in water.

### Step 2: Convert Volume of Water Displaced
The volume of water displaced is given as 100 ml. We need to convert this volume into cubic meters (m³) since SI units are required for calculations.

\[ 100 \text{ ml} = 100 \times 10^{-6} \text{ m}^3 = 10^{-4} \text{ m}^3 \]

### Step 3: Calculate the Weight of the Displaced Water
The weight of the water displaced can be calculated using the formula:

\[ \text{Weight of displaced water} = \text{Volume} \times \text{Density of water} \times g \]

Where:
- Volume = \(10^{-4} \text{ m}^3\)
- Density of water = \(1000 \text{ kg/m}^3\)
- \(g = 9.8 \text{ m/s}^2\)

Substituting the values:

\[ \text{Weight of displaced water} = 10^{-4} \text{ m}^3 \times 1000 \text{ kg/m}^3 \times 9.8 \text{ m/s}^2 \]

Calculating this gives:

\[ \text{Weight of displaced water} = 10^{-4} \times 1000 \times 9.8 = 0.98 \text{ N} \]

### Step 4: Calculate the Apparent Weight of the Ball
The apparent weight of the ball in water can be calculated using the formula:

\[ \text{Apparent weight} = \text{Weight of the ball} - \text{Weight of displaced water} \]

Substituting the values:

\[ \text{Apparent weight} = 5 \text{ N} - 0.98 \text{ N} = 4.02 \text{ N} \]

### Conclusion
The apparent weight of the ball when immersed in water is **4.02 N**.

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