Question

The dimensions of coefficient of viscosity are .............

• A. ML\(^{-1}\)T\(^{-1}\)
• B. ML\(^{-1}\)T\(^{-2}\)
• C. ML\(^{-2}\)T\(^{-2}\)
• D. ML\(^{-2}\)T\(^{-1}\)

Hint:

Viscosity is related to the resistance of a fluid to flow, and its dimensions can be derived using basic principles of force and velocity.

Answer 1

The Correct Option is A

Step 1: Understanding viscosity.
Viscosity is a measure of a fluid's resistance to deformation. The dimensions of viscosity can be derived using dimensional analysis, considering the units of force and velocity in fluid dynamics.
Step 2: Analyzing the options.
(A) ML\(^{-1}\)T\(^{-1}\): Correct — This is the correct dimensional formula for viscosity, derived from the relation \(\eta = \frac{F}{A \cdot v}\), where \(\eta\) is the viscosity, \(F\) is force, \(A\) is area, and \(v\) is velocity.
(B) ML\(^{-1}\)T\(^{-2}\): Incorrect — This does not match the dimensions of viscosity.
(C) ML\(^{-2}\)T\(^{-2}\): Incorrect — This is not the correct dimensional formula for viscosity.
(D) ML\(^{-2}\)T\(^{-1}\): Incorrect — This is also incorrect for viscosity.
Step 3: Conclusion.
The correct answer is (A) ML\(^{-1}\)T\(^{-1}\), as this represents the dimensional formula for viscosity.