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 $a$?

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

Unit of moment of inertia in MKS system

A physical quantity u is given by the relation $u = \frac{{{B^2}}}{{2{{\rm{\mu }}_0}}}$ here, B=magnetic field strength ${{\rm{\mu }}_0} =$ magnetic permeability of vacuum.

SI unit of permittivity is

The unit of potential energy is

If the units of M and L are increased three times, then the unit of energy will be increased by

In the equation $F = ma$, if the unit of force ($F$) is newton (N), mass ($m$) is kilogram (kg), and acceleration ($a$) is $ms^{-2}$, is the equation dimensionally homogeneous?

If $x = a + bt^2$, where $x$ is in meters and $t$ is in seconds, what are the dimensions of $b$?

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

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 =