If A, B, C and D represent velocity,accelerat | vedclass

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(C) Given: $A = [LT^{-1}]$ (velocity),$B = [LT^{-2}]$ (acceleration),$C = [ML^2T^{-2}A^{-2}]$ (inductance),$D = [M^{-1}L^{-2}T^4A^2]$ (capacitance).We

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(C) Given: $A = [LT^{-1}]$ (velocity),$B = [LT^{-2}]$ (acceleration),$C = [ML^2T^{-2}A^{-2}]$ (inductance),$D = [M^{-1}L^{-2}T^4A^2]$ (capacitance).We need to find the dimensions of $A^{-1} BCD$.Substitute the dimensions:$A^{-1} = [L^{-1}T]$$B = [LT^{-2}]$$C = [ML^2T^{-2}A^{-2}]$$D = [M^{-1}L^{-2}T^4A^2]$Now,calculate the product:$A^{-1} BCD = [L^{-1}T] \cdot [LT^{-2}] \cdot [ML^2T^{-2}A^{-2}] \cdot [M^{-1}L^{-2}T^4A^2]$Group the terms:$= [L^{-1} \cdot L \cdot L^2 \cdot L^{-2}] \cdot [T \cdot T^{-2} \cdot T^{-2} \cdot T^4] \cdot [M \cdot M^{-1}] \cdot [A^{-2} \cdot A^2]$$= [L^0] \cdot [T^1] \cdot [M^0] \cdot [A^0]$$= [T]$Thus,the expression has the dimensions of Time.

If $A, B, C$ and $D$ represent velocity,acceleration,inductance and capacitance respectively,then $A^{-1} BCD$ has the dimensions of

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