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Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.

It is true that the precise measurements of physical quantities is very essential for science. For instance, laser length measurements require a precision in the order of Angstrom (1 Å = 10–10 m). In satellite launching through space rockets, time is an important factor and is measured up to a precision of the order of 1 micro second (1μs = 10-6 s). Mass of sub-atomic particles are measured in the order of 10-30 kg. Inter-atomic spacing is measured in the order of a few Angstroms which needs to be precise to avoid errors in spectroscopy.


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19

The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit � 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres?

 20

The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

 22

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

A. the total mass of rain-bearing clouds over India during the Monsoon


B. the mass of an elephant


C. the wind speed during a storm


D. the number of strands of hair on your head


E. the number of air molecules in your classroom.

 23

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding

107 K, and its outer surface at a temperature of about 6000 K. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data: mass of the Sun = 2.0 ×1030 kg, radius of the Sun = 7.0 × 108 m.