Which of the following is not a dimensionless quantity?
Relative magnetic permeability $\left(\mu_{{r}}\right)$
Power factor
Permeability of free space $\left(\mu_{0}\right)$
Quality factor
The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$
where $p =$ pressure, $\rho =$ density, $v =$ speed, $h =$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant. The dimensional formula for $k$ is same as that for
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 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
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
Match List $I$ with List $II$
List $I$ | List $II$ |
$(A)$ Young's Modulus $(Y)$ | $(I)$ $\left[ M L ^{-1} T ^{-1}\right]$ |
$(B)$ Co-efficient of Viscosity $(\eta)$ | $(II)$ $\left[ M L ^2 T ^{-1}\right]$ |
$(C)$ Planck's Constant $(h)$ | $(III)$ $\left[ M L ^{-1} T ^{-2}\right]$ |
$(D)$ Work Function $(\phi)$ | $(IV)$ $\left[ M L ^2 T ^{-2}\right]$ |
Choose the correct answer from the options given below: