Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as
$\frac{h}{\varepsilon_{0} m_{e} c e^{2}}$
$\frac{\varepsilon_{0} m_{e} c e^{2}}{h}$
$\frac{h^{2}}{m_{e} c e^{2}}$
$\frac{m_{e} \varepsilon_{0}}{c e^{2}}$
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement 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 dimensional method, find the expression for $s$ is (Given that $\left.[s]=\left[ L ^2 T ^{-2} K ^{-1}\right]\right)$ is
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is