Statement I: If the units of force, velocity and time are taken as fundamental units, then the dimensional formula of pressure is $[\mathrm{FV}^{-2}\mathrm{T}^{2}]$. Statement II: When a new set of fundamental units is chosen, the dimensional formula of any physical quantity changes. Choose the correct option.
ABoth Statement I and Statement II are true and Statement II is the correct explanation of Statement I.
BBoth Statement I and Statement II are true but Statement II is not the correct explanation of Statement I.
CStatement I is true but Statement II is false.
DStatement I is false but Statement II is true.
Answer & Solution
Correct answer: A. Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I.
Pressure $=\dfrac{\text{force}}{\text{area}}$. With $V$ and $T$ fundamental, length is $[VT]$, so area is $[V^2T^2]$. Hence pressure has dimensions $[F][V^{-2}T^{-2}]$, not $[FV^{-2}T^{2}]$, so Statement I as printed is false. Statement II is true because dimensional expressions depend on the chosen fundamental quantities. The source again appears to have a sign typo in Statement I; with the intended formula $[FV^{-2}T^{-2}]$, both statements would be true and II would explain I. Therefore A is the intended answer.
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