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

If energy $E = G^p h^q c^r$,where $G$ is the universal gravitational constant,$h$ is Planck's constant,and $c$ is the speed of light,find the values of $p, q$,and $r$ respectively.

If $E$,$L$,$m$ and $G$ denote the quantities as energy,angular momentum,mass and constant of gravitation respectively,then the dimensions of $P$ in the formula $P = EL^2 m^{-5} G^{-2}$ are

Density of a liquid in $CGS$ system is $0.625 \ g/cm^3$. What is its magnitude in $SI$ system?

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

$A$ beaker contains a fluid of density $\rho \, kg/m^3$,specific heat $S \, J/kg \, ^\circ C$,and viscosity $\eta$. The beaker is filled up to height $h$. To estimate the rate of heat transfer per unit area $(Q/A)$ by convection when the beaker is placed on a hot plate,a student proposes that it should depend on $\eta$,$\left( \frac{S\Delta \theta}{h} \right)$,and $\left( \frac{1}{\rho g} \right)$,where $\Delta \theta$ (in $^\circ C$) is the temperature difference between the bottom and top of the fluid. In that situation,the correct option for $(Q/A)$ is: