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:

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

The damping force of an oscillating particle is observed to be proportional to velocity. The constant of proportionality can be measured in

The surface tension of a liquid is 70 dyne/cm, in MKS system value is

The unit of potential energy is

If 1 g cm ${{\rm{s}}^{ - 1}} = x$ newton-second, then the number x is equal to

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

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

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

There are atomic clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$. If two such clocks are operated with precision, then after running for 5000 years, these will record

If the unit of length and force be increased four times, then the unit of energy is