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

In the expression $P = El^2m^{-5}G^{-2}$,$E$,$l$,$m$ and $G$ denote energy,angular momentum,mass and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

Given that $v$ is speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

$A$ physical quantity $x$ is represented by the formula $x = M^a L^b T^c$. If $c \neq 0$,then:

Consider a simple pendulum,having a bob attached to a string,that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$,mass of the bob $(m)$,and acceleration due to gravity $(g)$. Derive the expression for its time period using the method of dimensions.

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)