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:

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

What will be the unit of time in that system in which the unit of length is metre, unit of mass is kg and unit of force is kg wt?

Let L denote the self-inductance of coil which is in series with a capacitor of capacitance C. Which of the following has the unit second?

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}} + kx$, where $l$ is the length, $g$ is acceleration due to gravity, and $x$ is displacement. The dimensions of $k$ are:

If the units of mass, length and time are doubled, unit of angular momentum will be

If the units of mass, length and time are doubled, unit of angular momentum will be

If the speed $v$ of transverse waves on a stretched string depends on the tension $T$ in the string and the mass per unit length $μ$ of the string, which of the following is dimensionally consistent?

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

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

Which of the following equations is dimensionally inconsistent?