In the equation $y = pq$ $tan\,(qt)$, $y$ represents position, $p$ and $q$ are unknown physical quantities and $t$ is time. Dimensional formula of $p$ is
${L^{1}}{T^{ - 1}}$
${L^1}{T^1}$
${L^{ - 1}}{T^1}$
${L^{ - 1}}{T^{ - 1}}$
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-
A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $(\tau )$. Dimensionally $\tau $ can be represented by
Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]