Dimensional Analysis — MCQ Practice

The dimensional formula for the coefficient of viscosity ($\eta$) is given by $F = \eta A \frac{dv}{dx}$, where $F$ is force, $A$ is area, $dv$ is change in velocity, and $dx$ is change in distance. What is the dimensional formula for $\eta$?

Which of the following pairs of physical quantities have the same dimensions?

If the velocity of light (c), Planck's constant (h), and Gravitational constant (G) are chosen as fundamental units, then the dimensions of mass in this new system would be:

In the equation $P + \frac{a}{V^2} = b\theta$, where $P$ is pressure, $V$ is volume, and $\theta$ is absolute temperature. If $a$ and $b$ are constants, what are the dimensions of $a$?

A physical quantity $X$ is given by $X = \frac{F L^2}{W}$, where $F$ is force, $L$ is length, and $W$ is work. What are the dimensions of $X$?

The equation of a wave is given by $y = A \sin(\omega t - kx)$, where $y$ is displacement, $t$ is time, and $x$ is distance. What are the dimensions of $\omega$ and $k$ respectively?

The energy of a photon is given by $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency. What is the dimensional formula for Planck's constant ($h$)?