If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is

The amount of heat energy $Q$ used to heat up a substance depends on its mass $m$,its specific heat capacity $s$,and the change in temperature $\Delta T$ of the substance. Using the dimensional method,find the expression for $s$. (Given that $[s] = [L^2 T^{-2} K^{-1}]$)

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:

$A$ physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$. Then the value of $\frac{a+b}{c+b}-d$ is

The equation of state for some gases is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P$ is pressure,$V$ is volume,$T$ is absolute temperature,and $a, b, R$ are constants. What are the dimensions of '$a$'?