5. Water is filled in a flask upto a height of 20 cm. The bottom of the flask is circular with radius 10 cm. If the atmospheric pressure is 1.013 × 105 Pa, find the force exerted by the water on the bottom. Take 8 = 10 ms and density of water = 1000 kgm™³.
Question
- Water is filled in a flask upto a height of 20 cm. The bottom of the flask is circular with radius 10 cm. If the atmospheric pressure is 1.013 × 105 Pa, find the force exerted by the water on the bottom. Take 8 = 10 ms and density of water = 1000 kgm™³.
Solution
To solve this problem, we need to use the formula for pressure at a depth in a fluid, which is given by P = P₀ + ρgh, where:
- P is the total pressure at the depth,
- P₀ is the atmospheric pressure,
- ρ is the density of the fluid,
- g is the acceleration due to gravity, and
- h is the depth in the fluid.
We also need to use the formula for the force exerted by a fluid, which is given by F = PA, where:
- F is the force,
- P is the pressure, and
- A is the area over which the pressure is exerted.
Step 1: Calculate the total pressure at the bottom of the flask.
P = P₀ + ρgh P = 1.013 × 10^5 Pa + (1000 kg/m³)(10 m/s²)(0.2 m) P = 1.013 × 10^5 Pa + 2000 Pa P = 1.015 × 10^5 Pa
Step 2: Calculate the area of the bottom of the flask.
A = πr² A = π(0.1 m)² A = 0.0314 m²
Step 3: Calculate the force exerted by the water on the bottom of the flask.
F = PA F = (1.015 × 10^5 Pa)(0.0314 m²) F = 3187 N
So, the force exerted by the water on the bottom of the flask is 3187 N.
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