H C Verma Solutions for Chapter: Introduction to Physics, Exercise 1: QUESTIONS FOR SHORT ANSWER

The meter is defined as the distance travelled by light in $\frac{1}{299,792,458}$ second. Why didn't people choose some easier number such as $\frac{1}{300,000,000}$ second? Why not $1$ second?

What are the dimensions of

$\left(\mathrm{a}\right)$ the volume of a cube of edge $a$?

$\left(\mathrm{b}\right)$ the volume of a sphere of radius $a$?

$\left(\mathrm{c}\right)$ the ratio of the volume of a cube of edge $a$ to the volume of a sphere of radius $a$?

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a metre stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?
 

If all the terms in an equation have the same units, is it necessary that they have the same dimensions? If all the terms in an equation have the same dimensions, is it necessary that they have the same units?

If two quantities have the same dimensions, do they represent the same physical content?
 

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use the foot of a person as a standard unit of length, which of the above features are present and which are not?
 

Suggest a way to measure:

$\left(\mathrm{a}\right)$ the thickness of a sheet of paper and

$\left(\mathrm{b}\right)$ the distance between the sun and the moon.