In the relation $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be
In the relation $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be
- [IIT 2004]
- A
$[{M^0}{L^2}{T^0}]$
- B
$[{M^1}{L^2}{T^1}]$
- C
$[{M^1}{L^0}{T^{ - 1}}]$
- D
$[{M^0}{L^2}{T^{ - 1}}]$
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- [AIPMT 1992]
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Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$.If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as
$\frac{v}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$
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Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$.If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as
$\frac{v}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$
where, $k$ is a dimensionless constant. Correct value of $a, b$ and $c$ are
- [KVPY 2015]