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In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X$ is pressure, $Y$ is volume, $R$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is
AEnergy
BImpulse
CPressure gradient
DCoefficient of viscosity
(JEE MAIN-2023)
Solution
$X$ and $\frac{a}{Y^2}$ have same dimensions
$Y$ and $b$ have same dimensions
$\therefore[a] =\left[ ML ^5 T ^{-2}\right]$
${[b] } =\left[ L ^3\right]$
$\frac{[a]}{[b]} =\left[ ML ^2 T ^{-2}\right] \text { has dimensions of energy }$
$Y$ and $b$ have same dimensions
$\therefore[a] =\left[ ML ^5 T ^{-2}\right]$
${[b] } =\left[ L ^3\right]$
$\frac{[a]}{[b]} =\left[ ML ^2 T ^{-2}\right] \text { has dimensions of energy }$
Standard 11
Physics
