The equation of a wave is given by$Y = A\sin \omega \left( {\frac{x}{v} - k} \right)$where $\omega $ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is
$LT$
$T$
${T^{ - 1}}$
${T^2}$
Which of the following quantities has a unit but dimensionless?
The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V\, = \,\frac{{\pi p{r^4}}}{{8\eta l}}$ where $p$ is the pressure difference between the two ends of the pipe and $\eta $ is coefficent of viscosity of the liquid having dimensional formula $[M^1L^{-1}T^{-1}] $. Check whether the equation is dimensionally correct.
If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then