If energy (E), velocity (v), and force (F) ar | vedclass

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(A) Let the dimension of mass be $[M] = [E]^x [v]^y [F]^z$.Substituting the dimensions of each quantity:$[M] = [M L^2 T^{-2}]^x [L T^{-1}]^y [M L T^{-

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$E v^{-2}$

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(A) Let the dimension of mass be $[M] = [E]^x [v]^y [F]^z$.Substituting the dimensions of each quantity:$[M] = [M L^2 T^{-2}]^x [L T^{-1}]^y [M L T^{-2}]^z$$[M] = M^{x+z} L^{2x+y+z} T^{-2x-y-2z}$Comparing the powers of $M, L,$ and $T$ on both sides:For $M$: $x + z = 1$For $L$: $2x + y + z = 0$For $T$: $-2x - y - 2z = 0$From the third equation: $y = -2x - 2z = -2(x + z)$.Since $x + z = 1$, we get $y = -2(1) = -2$.Now, substitute $y = -2$ into the second equation: $2x - 2 + z = 0 \implies 2x + z = 2$.We have the system:$x + z = 1$$2x + z = 2$Subtracting the first from the second: $x = 1$.Then $z = 1 - x = 1 - 1 = 0$.Thus, $[M] = [E]^1 [v]^{-2} [F]^0 = [E v^{-2}]$.

If energy $(E)$, velocity $(v)$, and force $(F)$ are taken as fundamental quantities, what are the dimensions of mass?

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