Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is
$k{\rho ^{1/2}}{a^{3/2}}{\bf{/}}\sqrt T $
$k{\rho ^{3/2}}{a^{3/2}}/\sqrt T $
$k{\rho ^{1/2}}{a^{3/2}}/{T^{3/4}}$
$k{\rho ^{1/2}}{a^{1/2}}/{T^{3/2}}$
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
Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful
Which of the following is dimensionally correct