To determine the weight of a weightless rubber balloon containing 100 grams of water when it is submerged in water, we can follow these steps:
### Step 1: Understand the Forces Acting on the Balloon
When the balloon is in air, it has a weight due to the water inside it. The weight of the water can be calculated using the formula:
\[ \text{Weight} = \text{mass} \times g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
### Step 2: Calculate the Weight of the Water
The mass of the water in the balloon is given as 100 grams, which is equal to 0.1 kg. Therefore, the weight of the water when the balloon is in air is:
\[ \text{Weight of water} = 0.1 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 0.981 \, \text{N} \]
### Step 3: Consider the Balloon Submerged in Water
When the balloon is submerged in water, two forces act on it:
1. The downward force (weight of the water): \( 0.981 \, \text{N} \)
2. The upward buoyant force (thrust force) exerted by the water.
### Step 4: Calculate the Buoyant Force
The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the submerged object. Since the balloon is filled with water, the volume of water displaced is equal to the volume of the water in the balloon.
The density of water is approximately \( 1000 \, \text{kg/m}^3 \). The volume of 100 grams of water can be calculated as:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{0.1 \, \text{kg}}{1000 \, \text{kg/m}^3} = 0.0001 \, \text{m}^3 \]
The weight of the displaced water (buoyant force) is:
\[ \text{Buoyant force} = \text{Volume} \times \text{Density of water} \times g \]
\[ = 0.0001 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 = 0.981 \, \text{N} \]
### Step 5: Determine the Apparent Weight
The apparent weight of the balloon when submerged in water is given by the difference between the downward force (weight of the water) and the upward buoyant force:
\[ \text{Apparent weight} = \text{Weight of water} - \text{Buoyant force} \]
\[ = 0.981 \, \text{N} - 0.981 \, \text{N} = 0 \, \text{N} \]
### Conclusion
Thus, the weight of the rubber balloon containing 100 grams of water when submerged in water is **0 N**.
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