JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 1)
If momentum [P], area $$[\mathrm{A}]$$ and time $$[\mathrm{T}]$$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
$$\left[\mathrm{P} \,\mathrm{A}^{-1} \mathrm{~T}^{0}\right]$$
$$\left[\mathrm{P} \,\mathrm{A}\mathrm{~T}^{-1}\right]$$
$$\left[\mathrm{P}\,\mathrm{A}^{-1} \mathrm{~T}\right]$$
$$\left[\mathrm{P} \,\mathrm{A}^{-1} \mathrm{~T}^{-1}\right]$$
Explanation
$$[\eta ] = [M{L^{ - 1}}{T^{ - 1}}]$$
Now if $$[\eta ] = {[P]^a}{[A]^b}{[T]^c}$$
$$ \Rightarrow [M{L^{ - 1}}{T^{ - 1}}] = {[M{L^1}{T^{ - 1}}]^a}{[{L^2}]^b}{[T]^c}$$
$$ \Rightarrow a = 1,\,a + 2b = - 1,\, - a + c = - 1$$
$$ \Rightarrow a = 1,\,b = - 1,\,c = 0$$
$$ \Rightarrow [\eta ] = [P]{[A]^{ - 1}}{[T]^0}$$
$$ = [P{A^{ - 1}}{T^0}]$$
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