Dimensions of Energy – Rankers Physics

Dimensions: Practice Problem & Solution

If force \([F]\), acceleration \([A]\) and time \([T]\) are chosen as the fundamental physical quantities. Find the dimensions of energy.
\([F][A^{-1}][T]\)
\([F][A][T]\)
\([F][A][T^2]\)
\([F][A][T^1]\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

Energy has the dimensions of work, which is \(\text{Force} \times \text{displacement}\). Since displacement has the dimensions of \(text{acceleration} \times \text{time}^2 = [A][T^2]\), the dimensional formula of energy is \([F][A][T^2]\).

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