In a system of units,if force (F),acceleratio | vedclass

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(B) Let the dimensional formula of energy $(E)$ be expressed as $E = k F^a A^b T^c$,where $k$ is a dimensionless constant.The dimensions of the quanti

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$F A T^2$

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(B) Let the dimensional formula of energy $(E)$ be expressed as $E = k F^a A^b T^c$,where $k$ is a dimensionless constant.The dimensions of the quantities are:$[E] = [M L^2 T^{-2}]$$[F] = [M L T^{-2}]$$[A] = [L T^{-2}]$$[T] = [T]$Substituting these into the equation:$[M L^2 T^{-2}] = [M L T^{-2}]^a [L T^{-2}]^b [T]^c$$[M L^2 T^{-2}] = [M^a L^{a+b} T^{-2a-2b+c}]$Comparing the powers of $M$,$L$,and $T$ on both sides:For $M$: $a = 1$For $L$: $a + b = 2 \implies 1 + b = 2 \implies b = 1$For $T$: $-2a - 2b + c = -2 \implies -2(1) - 2(1) + c = -2 \implies -4 + c = -2 \implies c = 2$Thus,the dimensional formula of energy is $F^1 A^1 T^2$,which is $F A T^2$.

In a system of units,if force $(F)$,acceleration $(A)$,and time $(T)$ are taken as fundamental units,then the dimensional formula of energy is:

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