Question

The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is

• A. distance
• B. time
• C. temperature
• D. mass

Hint:

Use dimensional analysis by expressing each quantity in terms of its fundamental dimensions and simplifying. The square root of a dimension gives a new physical quantity.

Answer 1

The Correct Option is A

Step 1: Write dimensional formula for kinetic energy. \[ \text{Kinetic energy} = \frac{1}{2}mv^2 \Rightarrow [M^1 L^2 T^{-2}] \] Step 2: Write dimensional formula for surface tension. \[ \text{Surface tension} = \frac{\text{Force}}{\text{Length}} = \frac{MLT^{-2}}{L} = [M^1 L^0 T^{-2}] \] Step 3: Ratio of kinetic energy to surface tension: \[ \frac{[M L^2 T^{-2}]}{[M T^{-2}]} = [L^2] \] Step 4: Take square root of the ratio: \[ \sqrt{[L^2]} = [L] \] This is the dimensional formula of distance. % Final Answer \[ \boxed{\text{Distance}} \]