$A$ new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes $8 \; min$ and $20 \; s$ to cover this distance?

The new $SI$ unit of mass $1 \, kg$ is defined in terms of the difference in the masses of two ${}^{133}Cs_{55}$ atoms. One of these atoms is in its ground state and the other is in an excited state that has a frequency of excitation close to $9.2 \times 10^9 \, Hz$. The number of atoms required to get $1 \, kg$ of mass this way is of the order of (Planck's constant = $6.63 \times 10^{-34} \, J \cdot s$; mass of proton = $1.67 \times 10^{-27} \, kg$; Avogadro number = $6.02 \times 10^{23} \, \text{particles}$; speed of light = $3 \times 10^8 \, m/s$).

Density of wood is $0.5 \; g/cm^3$ in the $CGS$ system of units. The corresponding value in $MKS$ units is?

Write the relation between torr and millibar.

Why do we have different units for the same physical quantity?

The total plane angle subtended by a circle at its centre is ......... $rad$.