The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be
$[{M^0}L{T^{ - 1}}]$
$[M{L^0}{T^{ - 1}}]$
$[M{L^{ - 1}}{T^0}]$
$[{M^0}{L^0}{T^0}]$
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
What is Dimensional Analysis ? State uses of Dimensional Analysis.
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is