If force F,length L,and time T are taken as t | vedclass

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(A) The dimensional formula for density is $[M L^{-3}]$.Let the dimension of density be expressed as $[F^{a} L^{b} T^{c}]$.Since force $F = [M L T^{-2

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$[F L^{-4} T^{2}]$

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(A) The dimensional formula for density is $[M L^{-3}]$.Let the dimension of density be expressed as $[F^{a} L^{b} T^{c}]$.Since force $F = [M L T^{-2}]$,we can write $[M L T^{-2}]^{a} [L]^{b} [T]^{c} = [M L^{-3}]$.Equating the powers of $M, L,$ and $T$:For $M$: $a = 1$.For $L$: $a + b = -3$.For $T$: $-2a + c = 0$.Substituting $a = 1$ into the equations:$1 + b = -3 \implies b = -4$.$-2(1) + c = 0 \implies c = 2$.Thus,the dimension of density is $[F^{1} L^{-4} T^{2}]$.

If force $F$,length $L$,and time $T$ are taken as the fundamental quantities,then what will be the dimension of density?

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