If force (F),velocity (V),and time (T) are co | vedclass

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(B) The dimensional formula for density $(\rho)$ is $[M L^{-3}]$.Let the dimensional formula be expressed as $[\rho] = [F]^a [V]^b [T]^c$.Substituting

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$F V^{-4} T^{-2}$

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(B) The dimensional formula for density $(\rho)$ is $[M L^{-3}]$.Let the dimensional formula be expressed as $[\rho] = [F]^a [V]^b [T]^c$.Substituting the dimensions: $[M L^{-3}] = [M L T^{-2}]^a [L T^{-1}]^b [T]^c$.$[M L^{-3}] = [M^a L^{a+b} T^{-2a-b+c}]$.Comparing the powers of $M$,$L$,and $T$ on both sides:For $M$: $a = 1$.For $L$: $a + b = -3 \Rightarrow 1 + b = -3 \Rightarrow b = -4$.For $T$: $-2a - b + c = 0 \Rightarrow -2(1) - (-4) + c = 0 \Rightarrow -2 + 4 + c = 0 \Rightarrow 2 + c = 0 \Rightarrow c = -2$.Thus,the dimensional formula is $[F^1 V^{-4} T^{-2}]$.

If force $(F)$,velocity $(V)$,and time $(T)$ are considered as fundamental physical quantities,then the dimensional formula of density will be:

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