If Surface tension $(S)$, Moment of Inertia $(I)$ and Planck’s constant $(h)$, were to be taken as the fundamental units, the dimensional formula for linear momentum would be
JEE MAIN 2019, Diffcult
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$P = k\,{s^a}{i^b}{h^c}$
Where $k$ is dimensionless constant
$ML{T^{ - 1}} = {\left( {M{T^{ - 2}}} \right)^a}\left( {M{L^2}} \right){\left( {M{L^2}{T^{ - 1}}} \right)^c}$
$a + b + c = 1$
$2b + 2c = 1$
$- 2a - c = - 1$
$a = \frac{1}{2} ,b = \frac{1}{2} ,c = 0$
${S^{1/2}}{i^{1/2}}{h^0}$
Where $k$ is dimensionless constant
$ML{T^{ - 1}} = {\left( {M{T^{ - 2}}} \right)^a}\left( {M{L^2}} \right){\left( {M{L^2}{T^{ - 1}}} \right)^c}$
$a + b + c = 1$
$2b + 2c = 1$
$- 2a - c = - 1$
$a = \frac{1}{2} ,b = \frac{1}{2} ,c = 0$
${S^{1/2}}{i^{1/2}}{h^0}$
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