An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is
$M{L^{ - 1}}{T^{ - 1}}$
$ML{T^{ - 1}}$
${M^0}L{T^{ - 1}}$
$M{L^0}{T^{ - 1}}$
A quantity $x$ is given by $\left( IF v^{2} / WL ^{4}\right)$ in terms of moment of inertia $I,$ force $F$, velocity $v$, work $W$ and Length $L$. The dimensional formula for $x$ is same as that of
Position of a body with acceleration '$a$' is given by $x = K{a^m}{t^n},$ here $t$ is time. Find dimension of $m$ and $n$.
Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.
Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]