Question

A water tank is open at the top and has a hole of area \( 10^{-4} \, \text{m}^2 \) at the bottom. The height of the water column is 5 m. What is the speed of the water flowing out of the hole? (Take \( g = 10 \, \text{m/s}^2 \))

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 20 m/s

Hint:

Remember: Torricelli’s law is used to calculate the speed of a fluid flowing out of a hole: \( v = \sqrt{2gh} \).

Answer 1

The Correct Option is A

Given: Height of water column, \( h = 5 \, \text{m} \) 
Gravitational acceleration, \( g = 10 \, \text{m/s}^2 \) 

Step 1: Use Torricelli's Law According to Torricelli’s law, the speed \( v \) of a fluid flowing out of a hole is given by: \[ v = \sqrt{2gh} \] where: - \( g \) is the acceleration due to gravity, - \( h \) is the height of the water column. 
Step 2: Substitute the given values Substitute the given values into the equation: \[ v = \sqrt{2(10 \, \text{m/s}^2)(5 \, \text{m})} \] \[ v = \sqrt{100} = 10 \, \text{m/s} \] 

Answer: The correct answer is option (b): 10 m/s.