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:

The SI unit of length is the metre. Suppose we adopt a new unit of length which equal x metre. The area of $1{m^2}$ expressed in terms of the new unit has a magnitude

Electron – volt is the unit of energy (1 eV = 1.6 $imes {10^{ - 19}}J)$. in H-atom, the binding energy of electron in first orbit is 13.6 eV. The same in joule (J) is

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 ${u_1}\,and\,{u_2}$ are the units selected in two systems of measurement and ${n_1}\,and\,{n_2}$ their numerical values, then

In a new system of units, unit f mass is 10 kg, unit of length is 1 km and unit of time is 1 min. The value of 1 joule in this new hypothertical system is

The concorde is the fastest airlines used for commercial service. It can cruise at 1450 mile per hour (about two times the speed of sound or in other words mach 2). What is it in m/s?

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

One million electron $volt\;\left( {1\;MeV} \right)$ is equal to

What is the power of a 100 W bulb in CGS units?

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