QUESTIONS FOR SHORT ANSWER
1)The metre is defined as the distance travelled by light in 1/299,792,458 second. Why didn't people choose some easier number such as 1/300,000,000 second? Why not 1 second?
2) What are the dimensions of
(a) volume of a cube of edge a
(b) volume of a sphere of radius a
(c) the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?
3) 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?
4) If all the termsin an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?
5) If two quantities have same dimensions, do they representsame physical content?
6) It is desirable that the standards of units be easily available, invariable, indestructible and easily rproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are no?
7) Suggest a way to measur :
(a) the thickness of a sheet of paper,
(b) the distance between the sun and the moon.