The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are

Let us consider an equation

$\frac{1}{2} m v^{2}=m g h$

where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct. 

The velocity of a freely falling body changes as ${g^p}{h^q}$ where g is acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are

Position of a body with acceleration '$a$' is given by $x = K{a^m}{t^n},$ here $t$ is time. Find dimension of $m$ and $n$.

Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x,\,y$ and $z$ such that ${P^x}{Q^y}{c^z}$ is dimensionless, are