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. \( 10 \)
• B. \( 20 \)
• C. \( 25.5 \)
• D. \( 5 \)

Hint:

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.

Answer 1

The Correct Option is B

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 \( 20 \, \text{ms}^{-1} \).