Match the following two coloumns
Column $-I$ | Column $-II$ |
$(A)$ Electrical resistance | $(p)$ $M{L^3}{T^{ - 3}}{A^{ - 2}}$ |
$(B)$ Electrical potential | $(q)$ $M{L^2}{T^{ - 3}}{A^{ - 2}}$ |
$(C)$ Specific resistance | $(r)$ $M{L^2}{T^{ - 3}}{A^{ - 1}}$ |
$(D)$ Specific conductance | $(s)$ None of these |
$A \to q, B \to s, C \to r, D \to p$
$A \to q, B \to r, C \to p, D \to s$
$A \to p, B \to q, C \to s, D \to r$
$A \to p, B \to r, C \to q, D \to s$
Which of the following is dimensionally incorrect?
If force $(F)$, length $(L) $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be
The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):
$(a)$ $K=m^{2} v^{3}$
$(b)$ $K=(1 / 2) m v^{2}$
$(c)$ $K=m a$
$(d)$ $K=(3 / 16) m v^{2}$
$(e)$ $K=(1 / 2) m v^{2}+m a$
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.