The foundations of dimensional analysis were laid down by

In the equation $x = a + bt + ct^2$,where $x$ is in meters and $t$ is in seconds,find the units of $a, b,$ and $c$.

In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?

In the relation $P = \frac{\alpha}{\beta} e^{-\frac{\alpha Z}{k\theta}}$,$P$ is pressure,$Z$ is distance,$k$ is Boltzmann constant,and $\theta$ is temperature. The dimensional formula of $\beta$ is:

The equation of a stationary wave is $y = 2A \sin \left(\frac{2 \pi ct}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$. Which of the following statements is wrong?

The physical quantity which has the dimensional formula ${M^1}{T^{ - 3}}$ is