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

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.

Which of the following equations is dimensionally homogeneous?

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

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

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 $a$, $b$.

If the unit of force and length each be increased by four times, then the unit of energy is increased by

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

Volt/metre is the unit of

Light year is a unit of

Unit of moment of inertia in MKS system