If velocity v,acceleration A,and force F are | vedclass

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(B) Let the angular momentum $L$ be expressed as $L = k v^x A^y F^z$,where $k$ is a dimensionless constant.Substituting the dimensions of each quantit

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$F v^3 A^{-2}$

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(B) Let the angular momentum $L$ be expressed as $L = k v^x A^y F^z$,where $k$ is a dimensionless constant.Substituting the dimensions of each quantity:$[M L^2 T^{-1}] = [L T^{-1}]^x [L T^{-2}]^y [M L T^{-2}]^z$$[M L^2 T^{-1}] = M^z L^{x+y+z} T^{-x-2y-2z}$Comparing the exponents of $M, L$,and $T$ on both sides:For $M$: $z = 1$For $L$: $x + y + z = 2$For $T$: $-x - 2y - 2z = -1$Substituting $z = 1$ into the other equations:$x + y = 1$ (Equation $i$)$-x - 2y = 1$ (Equation $ii$)Adding $(i)$ and $(ii)$: $-y = 2 \Rightarrow y = -2$Substituting $y = -2$ into $x + y = 1$: $x - 2 = 1 \Rightarrow x = 3$Thus,the dimensional formula is $[L] = [F v^3 A^{-2}]$.

If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be

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