Question

Dimensions of the physical quantity $X$ in the equation \[ {Force} = \frac{X}{{Volume}} \] are

• A. $ML^3T^2$
• B. $MLT$
• C. $ML^2T^2$
• D. $MLT^{-2}$
• E. $ML^4T^{-2}$

Hint:

Use the fundamental dimensions of mass (M), length (L), and time (T) to verify dimensional consistency.

Answer 1

Answer: (E)

Step 1: The dimensional formula of Force is \[ {Force} = MLT^{-2} \] Step 2: The dimensional formula of Volume is \[ {Volume} = L^3 \] Step 3: From the equation \[ X = {Force} \times {Volume} \] \[ X = (MLT^{-2}) \times (L^3) = ML^4T^{-2} \] Step 4: Therefore, the correct answer is (E).