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:

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

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

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 = $= 1.67 imes {10^{ - 17}}kg$)

Consider a new system of units in which c(speed of light in vacuum), h(Planck’s constant) and G(gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?

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:

Given the equation $P = \frac{a}{V} - \frac{b}{V^2} + cT$, where $P$ is pressure, $V$ is volume, and $T$ is temperature. What are the dimensions of $abc$?

A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is $\alpha$ kg, the unit of length is $\beta$ metre and the unit of time is γ sec. In this new system. 1 calorie =

The velocity of a wave is given by $v = \sqrt{\frac{T}{\mu}} + ax^2$, where $T$ is tension, $\mu$ is linear density, and $x$ is displacement. What are the dimensions of $a$?

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:

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