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 the given fundamental physical quantities: Force [F], Acceleration [A], and Time [T], we need to express energy in terms of these quantities. 

Energy is typically defined as work done, which can be calculated using the formula:

\(\text{Energy} (E) = \text{Force} (F) \times \text{Distance} (d)\)

We know that:

• Force \([F]\) is already given as a fundamental quantity.
• Distance can be expressed as the product of Velocity and Time: \(d = v \times t\)

Also, Velocity \(v\) can be expressed in terms of Acceleration and Time:

\(v = A \times T\)

Substituting this into the distance formula:

\(d = (A \times T) \times T = A \times T^2\)

Thus, Energy becomes:

\(E = F \times d = F \times (A \times T^2) = F \times A \times T^2\)

Therefore, the dimensions of energy in terms of [F], [A], and [T] are:

\([F] [A] [T^2]\)

This matches the provided correct answer option: [F] [A] [T²].