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Assuming velocity (V) time (T) and force...

Assuming velocity (V) time (T) and force (F) as the fundamental quantities find the dimension of density.

Text Solution

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Dimension of velocity [V] = `LT^(-1)`, dimension of time [T] = T , dimension of force [F] = `MLT^(-2)` , dimension of density [D] = `ML^(-3)`
As the dimension of density does not involve T we have
`[D]=ML^(-3)= (MLT^(-2))/(L^(4)T^(-4)xxT^(2))`
`=([F])/([V]^(4).[T]^(2))=[F][V]^(-4)[T]^(-2)`
i.e., `FV^(-4)T^(-2)` is the dimension of density assuming V, T and F as the fundamental quantities.
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