Question

The dimensional formula of surface tension is:

• A. \( [L^{-1}M^1T^{-2}] \)
• B. \( [L^2M^1T^{-2}] \)
• C. \( [L^1M^1T^{-1}] \)
• D. \( [L^0M^1T^{-2}] \)

Hint:

Dimensional analysis is a useful tool for verifying equations and ensuring unit consistency in physics problems.

Answer 1

The Correct Option is D

Step 1: Surface tension is defined as the force per unit length: \[ T = \frac{{Force}}{{Length}}. \] The dimensional formula of force is: \[ [F] = M L T^{-2}. \] By dividing force by length (\( L \)), we obtain the dimensional formula for surface tension: \[ [T] = M L^{-1} T^{-2}. \] Step 2: After comparing with the given options, the correct answer is option (d).