AIIMS 2018 Physics Dimensional Analysis MCQ Question

In the context of fundamental units where force (F) is defined as mass (M) times acceleration (a), and acceleration is expressed as length (L) per time squared (T²), we can derive the dimensional formula for mass. Since $F = M \cdot \frac{L}{T^2}$, rearranging gives $M = F \cdot \frac{T^2}{L}$, leading to the dimensional formula $[FL^{-1}T^{2}]$. However, since mass is not a fundamental unit in this context, we express it in terms of the given fundamental units, resulting in $[FL^{-1}T^{-2}]$ for mass, which corresponds to option C.

Option A incorrectly suggests that mass is represented as $[FL^{-1}T^{2}]$, which does not align with the dimensional analysis. Options B and D are also incorrect as they do not accurately reflect the relationship between force, mass, and the fundamental units provided.