A rubber balloon has 200 g of water in it. Its weight in water will be (neglect the weight of balloon)

Options

A. 100 g
B. 200 g
C. 50 g
D. zero

Answer

To find the weight of the rubber balloon containing 200 g of water when it is submerged in water, we need to consider the concept of buoyancy and apparent weight. Here’s the step-by-step solution:

### Step 1: Understand the weight of the water
The weight of the water inside the balloon can be calculated using the formula:
\[ \text{Weight} = \text{mass} \times \text{gravitational acceleration} \]
Given that the mass of the water is 200 g (which is equivalent to 0.2 kg), and taking gravitational acceleration \( g \) as approximately \( 9.8 \, \text{m/s}^2 \):
\[ \text{Weight of water} = 0.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1.96 \, \text{N} \]

### Step 2: Calculate the buoyant force (up-thrust)
The buoyant force acting on the balloon when it is submerged in water is equal to the weight of the water displaced by the balloon. Since the volume of water in the balloon is equal to the volume of water displaced, we can use the density of water (\( \rho \)) which is approximately \( 1000 \, \text{kg/m}^3 \).

The volume of the water inside the balloon can be calculated as:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{0.2 \, \text{kg}}{1000 \, \text{kg/m}^3} = 0.0002 \, \text{m}^3 \]

Now, the buoyant force \( F_b \) can be calculated using:
\[ F_b = \text{density of water} \times g \times \text{volume displaced} \]
\[ F_b = 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 0.0002 \, \text{m}^3 = 1.96 \, \text{N} \]

### Step 3: Calculate the apparent weight
The apparent weight of the balloon in water is given by the formula:
\[ \text{Apparent weight} = \text{Weight of water} - \text{Buoyant force} \]
Substituting the values we calculated:
\[ \text{Apparent weight} = 1.96 \, \text{N} - 1.96 \, \text{N} = 0 \, \text{N} \]

### Conclusion
Thus, the weight of the rubber balloon with 200 g of water in it when submerged in water is **0 N**.