Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
- [AIPMT 1993]
- A
$\left[ {M{L}{T^{ - 1}}} \right]$
- B
$\left[ M^0L^0T^0 \right]$
- C
$\left[ {M{L^{ - 1}}{T^{ - 1}}} \right]$
- D
$\left[ {M{L^{ 2}}{T^{ - 2}}} \right]$
Similar Questions
The $SI$ unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............
The $SI$ unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............
- [JEE MAIN 2022]
Which one of the following is dimensionless physical quantity?
Which one of the following is dimensionless physical quantity?
If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x,\,y$ and $z$ such that ${P^x}{Q^y}{c^z}$ is dimensionless, are
If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x,\,y$ and $z$ such that ${P^x}{Q^y}{c^z}$ is dimensionless, are
- [AIPMT 1992]
What is the dimension of Luminous flux
What is the dimension of Luminous flux
- [AIIMS 2019]
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
- [JEE MAIN 2023]