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 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

Which does not have the same unit as others

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

The SI unit of electrochemical equivalent is

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?

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

Unit of magnetic moment is

Unit of moment of inertia in MKS system

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?

The viscous force $F$ acting on a sphere moving through a liquid depends on the radius $r$ of the sphere, the velocity $v$ of the sphere, and the coefficient of viscosity $η$ of the liquid. If $F = kη^arv^b$, where $k$ is a dimensionless constant, using dimensional analysis, find the values of $a$, $b$.