If force (F),velocity (V),and time (T) are ta | vedclass

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(D) Let mass $m \propto F^a V^b T^c$.Then $m = k F^a V^b T^c$,where $k$ is a dimensionless constant.Writing dimensions on both sides:$[M L^0 T^0] = [M

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

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(D) Let mass $m \propto F^a V^b T^c$.Then $m = k F^a V^b T^c$,where $k$ is a dimensionless constant.Writing dimensions on both sides:$[M L^0 T^0] = [M L T^{-2}]^a [L T^{-1}]^b [T]^c$$[M L^0 T^0] = [M^a L^{a+b} T^{-2a-b+c}]$Comparing the powers of $M, L,$ and $T$ on both sides:For $M$: $a = 1$For $L$: $a + b = 0 \implies 1 + b = 0 \implies b = -1$For $T$: $-2a - b + c = 0 \implies -2(1) - (-1) + c = 0 \implies -2 + 1 + c = 0 \implies c = 1$Substituting the values of $a, b,$ and $c$ in the equation,we get:$[m] = [F^1 V^{-1} T^1] = [F V^{-1} T]$.

If force $(F)$,velocity $(V)$,and time $(T)$ are taken as fundamental units,then the dimensions of mass are:

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