The velocity $v$ (in $cm/\sec $) of a particle is given in terms of time $t$ (in sec) by the relation $v = at + \frac{b}{{t + c}}$ ; the dimensions of $a,\,b$ and $c$ are
$a = {L^2},\,b = T,\,c = L{T^2}$
$a = L{T^2},\,b = LT,\,c = L$
$a = L{T^{ - 2}},b = L,\,c = T$
$a = L,\,b = LT,\,c = {T^2}$
Given that $v$ is the speed, $r$ is radius and $g$ is acceleration due to gravity. Which of the following is dimensionless?
An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.
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