If force [F],acceleration [A],and time [T] ar | vedclass

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(B) Let the energy $E$ be expressed as $E = k F^{a} A^{b} T^{c}$,where $k$ is a dimensionless constant.The dimensional formula for energy is $[M^{1} L

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$[F][A][T^{2}]$

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(B) Let the energy $E$ be expressed as $E = k F^{a} A^{b} T^{c}$,where $k$ is a dimensionless constant.The dimensional formula for energy is $[M^{1} L^{2} T^{-2}]$.The dimensional formula for force is $[M^{1} L^{1} T^{-2}]$.The dimensional formula for acceleration is $[L^{1} T^{-2}]$.The dimensional formula for time is $[T^{1}]$.Substituting these into the equation:$[M^{1} L^{2} T^{-2}] = [M^{1} L^{1} T^{-2}]^{a} [L^{1} T^{-2}]^{b} [T^{1}]^{c}$$[M^{1} 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 $L$: $a + b = 2 \Rightarrow 1 + b = 2 \Rightarrow b = 1$For $T$: $-2a - 2b + c = -2 \Rightarrow -2(1) - 2(1) + c = -2 \Rightarrow -4 + c = -2 \Rightarrow c = 2$Thus,the dimensions of energy in terms of $F, A,$ and $T$ are $[F^{1} A^{1} T^{2}]$ or $[F][A][T^{2}]$.

If force $[F]$,acceleration $[A]$,and time $[T]$ are chosen as the fundamental physical quantities,find the dimensions of energy.

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