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

Match the following two coloumns

  Column $-I$   Column $-II$
$(A)$ Electrical resistance $(p)$ $M{L^3}{T^{ - 3}}{A^{ - 2}}$
$(B)$ Electrical potential $(q)$ $M{L^2}{T^{ - 3}}{A^{ - 2}}$
$(C)$ Specific resistance $(r)$ $M{L^2}{T^{ - 3}}{A^{ - 1}}$
$(D)$ Specific conductance $(s)$ None of these

A physcial quantity $x$ depends on quantities $y$ and $z$ as follows: $x = Ay + B\tan Cz$, where $A,\,B$ and $C$ are constants. Which of the following do not have the same dimensions

A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by

  • [IIT 1992]

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.

If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then

  • [JEE MAIN 2015]