Step 1: Problem Definition
A cylinder contains water at a height of 20 m. A small aperture near the base is opened, and the water's exit velocity is to be determined.
Step 2: Torricelli's Law Application
The velocity of efflux (\( v \)) from a small opening at the base of a container is quantified by Torricelli's Law:\[v = \sqrt{2gh}\]where:
\( g \) = acceleration due to gravity (\( 10 \, \text{ms}^{-2} \)),
\( h \) = fluid column height above the opening (20 m).
Step 3: Velocity Calculation
Inputting values into the formula:\[v = \sqrt{2 \times 10 \times 20}\]\[v = \sqrt{400} = 20 \text{ m/s}\]
Step 4: Option Selection
The matching option is (b) 20.Final Answer: The calculated efflux velocity of water is \( 20 \, \text{ms}^{-1} \).