The physical quantities not having same dimensions are
Speed and ${({\mu _0}{\varepsilon _0})^{ - 1/2}}$
Torque and work
Momentum and Planck's constant
Stress and Young's modules
The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is
The pair(s) of physical quantities that have the same dimensions, is (are)
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is
If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimension as that the $\sqrt{\mathrm{uG}}$ :
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$