Question

A liquid is filled upto a height of 20 cm in a cylindrical vessel. The speed of liquid coming out of a small hole at the bottom of the vessel is (g = 10 ms\(^{-2}\))

• A. 1.2 ms\(^{-1}\)
• B. 1 ms\(^{-1}\)
• C. 2 ms\(^{-1}\)
• D. 3.2 ms\(^{-1}\)
• E. 1.4 ms\(^{-1}\)

Hint:

For efflux problems, always convert height into meters before using \(v = \sqrt{2gh}\).

Answer 1

The Correct Option is C

Concept: According to Torricelli’s theorem: \[ v = \sqrt{2gh} \] This is derived from Bernoulli’s principle assuming negligible viscosity and atmospheric pressure at both points.

Step 1: Convert height into SI units. \[ h = 20 \, \text{cm} = 0.2 \, \text{m} \]

Step 2: Substitute values into formula. \[ v = \sqrt{2 \times 10 \times 0.2} \]

Step 3: Simplify. \[ v = \sqrt{4} = 2 \, \text{m/s} \]

Step 4: Conclusion. \[ \boxed{2 \, \text{m/s}} \]