Question

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy

• A. [F] [A⁻¹] [T]
• B. [F] [A] [T]
• C. [F] [A] [T²]
• D. [F] [A] [T⁻¹]

Answer 1

The Correct Option is C

To find the dimensions of energy using force [F], acceleration [A], and time [T] as the fundamental physical quantities, we need to express energy in terms of these chosen fundamentals.

Step-by-Step Explanation

1. Basic Definition: The dimensional formula for energy is given by the definition of energy, which is the capacity to do work.
2. Relation with Work: Energy is often equated to work done, which is expressed as the product of force and displacement.
3. Formula for Work Done: The work done, or energy, \(E\) is given by: \(E = F \cdot s\) where \(s\) is the displacement.
4. Displacement in terms of Acceleration and Time: Using the equation of motion, displacement \(s\) for constant acceleration can be derived as: \(s = \frac{1}{2} A T^2\), where \(A\) is acceleration and \(T\) is time.
5. Substitute Displacement: Replace \(s\) in the work formula: \(E = F \cdot \left(\frac{1}{2} A T^2\right)\)
6. Simplifying: Simplifying the equation, we get: \(E = \frac{1}{2} F A T^2\) This shows that the dimensions of energy are proportional to: \([F][A][T^2]\)

Thus, the correct dimensional formula for energy, in terms of the chosen fundamental quantities, is:

Correct Answer: \([F][A][T^2]\)