The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

In a certain system of units,one unit of mass is $50 \ g$,one unit of length is $10 \ cm$,and one unit of time is $5 \ s$. Then,in this system,$1$ unit of pressure equals to :-

$A$ great physicist of this century ($P.A.M.$ Dirac) loved playing with numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics ($c, e,$ mass of electron, mass of proton) and the gravitational constant $G$, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe ($\approx 15$ billion years). From the table of fundamental constants in this book, try to see if you too can construct this number. If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

Force is given by the expression, $F = A \cos(Bx) + C \cos(Dt)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is the same as that of

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$ respectively. Here $m$ and $n$ are constants. The relations for distance $(L)$ and time $(T)$ in the two systems are: