The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
${M^0}{L^0}{T^0}$
${M^0}{L^0}{T^{ - 1}}$
${M^0}{L^{ - 1}}{T^0}$
${M^0}{L^1}{T^{ - 1}}$
The dimensions of Planck's constant and angular momentum are respectively
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
Given that $v$ is the speed, $r$ is radius and $g$ is acceleration due to gravity. Which of the following is dimensionless?
A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon _0}$ is $[c$ is velocity of light, $G$ is the universal constant of gravitation and $e$ is charge $] $
Dimensions of potential energy are