The speed of sound in a medium depends on the modulus of elasticity $E$ and density $\rho$ of the medium. Using dimensional analysis, determine the relationship between these quantities.

A physical quantity of the dimensions of length that can be formed out of $c$, $G$ and $\frac{e^2}{4\pi \varepsilon_0}$ is [where $c$ is velocity of light, $G$ is universal constant of gravitation and $e$ is charge]

Planck’s constant $(h)$, speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has dimension of length?

If the unit of force is 'N', the unit of acceleration is 'm/s$^2$', and the unit of time is 's', what is the unit of energy?

In the gas equation $\left( {p + \frac{a}{{{V^2}}}} \right)\left( {V - b} \right) = RT,$, the dimensions of a are

$E,m,I\;{\rm{and}}\;G$ denote energy, mass, angular momentum and gravitational constant respectively, then the dimensions of $\frac{{E{I^2}}}{{{m^5}{G^2}}}$ are

Given Planck's constant ($h$), speed of light ($c$), and Newton's gravitational constant ($G$), determine the combination resulting in a quantity with dimensions of mass.

In ${\rm{\;S}} = a + bt + c{t^2}$. S is measured in metre and t in second. The unit of c is

The speed of sound in a medium depends on the modulus of elasticity $E$ and density $\rho$ of the medium. Using dimensional analysis, determine the relationship between these quantities.

Given, Force $= \frac{\alpha }{{{\rm{density}} + {\rm{\;}}{{\rm{\beta }}^3}}}$ What are the dimensions of ${\rm{\alpha }},{\rm{\beta }}?$

$X = 3Y{Z^2}$ find dimension of Y in (MKS) system, If X and Z are the dimensions of capacity and magnetic field respectively