A hypothetical equation is given as $\rho = a \sqrt{P} + bT^2$, where $\rho$ is density, $P$ is pressure, and $T$ is temperature. The dimensions of $\frac{a}{b}$ are:

One femtometre is equivalent to

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

One is equivalent to 931 MeV energy. The rest mass of electron is $9.1 imes {10^{ - 31}}kg$. the Mass equivalent energy is (1 amu = $= 1.67 imes {10^{ - 17}}kg$)

Which is different from others by units

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

One  light  year  is defined as the distance travelled by light in one year. The speed of light is $3 imes {10^8}{\rm{m}}{{\rm{s}}^{ - 1}}$. The same in metre is

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

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

One slug is equivalent to 14.6 kg. A force of 10 pound is applied on a body of 1 kg. The acceleration of the body is

The unit of potential energy is