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 cannot be regarded as an essential characteristic of a unit of measurement?

Unit of magnetic moment is

Which of the following is not the unit of energy

If the speed $v$ of transverse waves on a stretched string depends on the tension $T$ in the string and the mass per unit length $μ$ of the string, which of the following is dimensionally consistent?

Which does not have the same unit as others

Oersted is a unit of

If the acceleration due to gravity is 10$\;{\rm{m}}{{\rm{s}}^{ - 2}}$ and the units of length and time are changed in kilometer and hour respectively, the numerical value of acceleration is

The unit of permittivity of free space ${\varepsilon _0}$ is

Assuming the mass of Earth as $6.64 imes {10^{24}}kg$ and the average mass of the atoms that make up earth as 40u (atomic mass unit), the number of atoms in the Earth are approximately

The time period ($T$) of a simple pendulum depends on its length ($l$) and acceleration due to gravity ($g$). Which of the following is dimensionally consistent with the principle of homogeneity?