If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.
A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$
$(b)\;y=a \sin v t$
$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.
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
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$.If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as
$\frac{v}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$
where, $k$ is a dimensionless constant. Correct value of $a, b$ and $c$ are