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:

Wavelength of ray of light is 0.00006 m. It is equal to

Which of the following is not equal to watt

Which of the following system of units is not based on units of mass, length and time alone

Length is measured in metre and time in second as usual. But a new unit of mass is so chosen that G=1. This new unit of mass is equal to

The time taken by an electron to go from ground state to excited state is one shake (one shake = ${10^{ - 8}}$ s) this time in nanosecond will be

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?

Oersted is a unit of

The frequency $ν$ of vibration of a stretched string depends on its length $l$, its linear mass density $μ$, and its tension $T$. Which of the following is a possible formula for $ν$, consistent with the principle of homogeneity?

Temperature can be expressed as a derived quantity in terms of any of the following

A pressure of ${10^6}$ dyne ${\rm{c}}{{\rm{m}}^{ - 2}}$ is equivalent to