The principle of homogeneity states that:

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

Which of the following is not a valid application of the principle of homogeneity?

The unit of surface tension in SI system is

In the equation $F = ma$, if the unit of force ($F$) is newton (N), mass ($m$) is kilogram (kg), and acceleration ($a$) is $ms^{-2}$, is the equation dimensionally homogeneous?

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left( { = 0.5^\circ } \right),$ then the least count of the instrument is

How many wavelengths of $K{r^{86}}{\rm{\;}}$ are there in one metre

The unit of potential energy is

The unit of angular acceleration in the SI system is

Let L denote the self-inductance of coil which is in series with a capacitor of capacitance C. Which of the following has the unit second?

Density of liquid in CGS system is $0.625{\rm{\;\;g\;c}}{{\rm{m}}^{ - 3}}.$. What is its magnitude in SI system?