Question

The dimensional formula of force is: ____.

• A. [MLT⁻¹]
• B. [ML²T⁻²]
• C. $[MLT^{-2}]$
• D. [M⁰LT⁻²]

Hint:

$[MLT^{-2}]$ is one of the most important dimensional formulas in physics. Many other quantities like Work, Energy ($ML^2T^{-2}$), and Pressure ($ML^{-1}T^{-2}$) are derived directly from it.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A dimensional formula expresses a physical quantity in terms of the fundamental units of Mass ($M$), Length ($L$), and Time ($T$).

Step 2: Key Formula or Approach:
According to Newton's Second Law: \[ \text{Force} (F) = \text{mass} (m) \times \text{acceleration} (a) \]

Step 3: Detailed Explanation:
1. Dimensions of Mass ($m$) = $[M]$ 2. Acceleration is change in velocity per unit time: \[ a = \frac{v}{t} = \frac{\text{Length/Time}}{\text{Time}} = [LT^{-2}] \] 3. Multiplying them together: \[ [F] = [M] \times [LT^{-2}] = [MLT^{-2}] \]

Step 4: Final Answer:
The dimensional formula of force is $[MLT^{-2}]$.