Question:
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms\(^{-1}\)) through a small hole on the side wall of the cylinder near its bottom is:
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms\(^{-1}\)) through a small hole on the side wall of the cylinder near its bottom is:
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Torricelli's Theorem states that the velocity of a fluid exiting a hole under the influence of gravity is equivalent to the velocity an object would attain if it fell freely from the same height.
Updated On: Feb 12, 2025
- \( 10 \)
- \( 20 \)
- \( 25.5 \)
- \( 5 \)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Problem
We have a cylinder filled with water to a height of 20 m. A small hole is made near the bottom of the cylinder, and we need to find the velocity of efflux of water through this hole.
Step 2: Applying Torricelli's Law
The velocity of efflux (\( v \)) of a fluid through a small hole at the bottom of a container is given by Torricelli's Theorem: \[ v = \sqrt{2gh} \] where:
\( g \) is the acceleration due to gravity (\( 10 \, \text{ms}^{-2} \)),
\( h \) is the height of the fluid column above the hole (20 m in this case).
Step 3: Calculating the Velocity
Substitute the values into the formula: \[ v = \sqrt{2 \times 10 \times 20} \] \[ v = \sqrt{400} = 20 \text{ m/s} \]
Step 4: Matching with the Options
The correct option is (b) 20. Final Answer: The velocity of efflux of water is \( 20 \, \text{ms}^{-1} \).
We have a cylinder filled with water to a height of 20 m. A small hole is made near the bottom of the cylinder, and we need to find the velocity of efflux of water through this hole.
Step 2: Applying Torricelli's Law
The velocity of efflux (\( v \)) of a fluid through a small hole at the bottom of a container is given by Torricelli's Theorem: \[ v = \sqrt{2gh} \] where:
\( g \) is the acceleration due to gravity (\( 10 \, \text{ms}^{-2} \)),
\( h \) is the height of the fluid column above the hole (20 m in this case).
Step 3: Calculating the Velocity
Substitute the values into the formula: \[ v = \sqrt{2 \times 10 \times 20} \] \[ v = \sqrt{400} = 20 \text{ m/s} \]
Step 4: Matching with the Options
The correct option is (b) 20. Final Answer: The velocity of efflux of water is \( 20 \, \text{ms}^{-1} \).
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