If velocity [V],time [T],and force [F] are ch | vedclass

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(A) Let the dimension of mass be represented as $[M] = [F]^a [T]^b [V]^c$.Substituting the dimensions of the base quantities:$[M^1 L^0 T^0] = [M^1 L^1

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$[F T V^{-1}]$

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(A) Let the dimension of mass be represented as $[M] = [F]^a [T]^b [V]^c$.Substituting the dimensions of the base quantities:$[M^1 L^0 T^0] = [M^1 L^1 T^{-2}]^a [T^1]^b [L^1 T^{-1}]^c$$[M^1 L^0 T^0] = [M^a L^{a+c} T^{-2a+b-c}]$Comparing the powers of $M, L,$ and $T$ on both sides:For $M$: $a = 1$For $L$: $a + c = 0 \implies 1 + c = 0 \implies c = -1$For $T$: $-2a + b - c = 0 \implies -2(1) + b - (-1) = 0 \implies -2 + b + 1 = 0 \implies b = 1$Therefore,the dimensions of mass are $[F^1 T^1 V^{-1}]$,which is written as $[F T V^{-1}]$.

If velocity $[V]$,time $[T]$,and force $[F]$ are chosen as the base quantities,the dimensions of mass will be:

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