NCERT Solutions for Chapter: Units and Measurement, Exercise 3: VSA

Why do we have different units for same physical quantity?

The radius of atom is of the order of 1 $1 Å$and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?

Name the device used for measuring the mass of atoms and molecules.

Express unified atomic mass unit in kg.

A function $f\left(\theta \right)$ is defined as:

$f\left(\theta \right)=1-\theta +\frac{{\theta }^2}{2!}-\frac{{\theta }^2}{3!}+\frac{{\theta }^4}{4!}-\dots \dots$

Why is it necessary for $f\left(\theta \right)$ to be a dimensionless quantity?

Why length, mass and time are chosen as base quantities in mechanics?