# NCERT Physics Class 11 Exemplar Chapter 2 Units And Measurements Part-5

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41). An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that

where k is a dimensionless constant and g is acceleration due to gravity.

Explanation: Given . T is also function of g and

For

For T, Therefore,

Thus,

42). In an experiment to estimate the size of a molecule of oleic acid 1 mL of oleic acid is dissolved in 19 mL of alcohol. Then 1 mL of this solution is diluted to 20 mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film which will give us the size of oleic acid molecule.

Read the passage carefully and answer the following questions:

Why do we dissolve oleic acid in alcohol?

Explanation: Because oleic acid dissolves in alcohol but does not dissolve in water

What is the role of lycopodium powder?

Explanation: When lycopodium powder is spread on water, it spreads on the entire surface. When a drop of the prepared solution is dropped on water, oleic acid does not dissolve in water, it spreads on the water surface pushing the lycopodium powder away to clear a circular area where the drop falls. This allows measuring the area where oleic acid spreads

What would be the volume of oleic acid in each mL of solution prepared?

Explanation:

How will you calculate the volume of n drops of this solution of oleic acid?

Explanation: By means of a burette and measuring cylinder and measuring the number of drops.

What will be the volume of oleic acid in one drop of this solution?

Explanation: If n drops of the solution make 1 mL, the volume of oleic acid in one drop will be

43 (a) How many astronomical units (A.U.) make 1 parsec?

Explanation: By definition of parsec

(b) Consider a sun like star at a distance of 2 parsecs. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be from the earth. Due to atmospheric fluctuations, eye can’t resolve objects smaller than 1 arc minute.

Explanation: At 1 A.U. distance, sun is (1/2°) in diameter.

Therefore, at 1 parsec, star is degree in diameter = arcmin. With 100 magnification, it should look arcmin. However, due to atmospheric fluctuations, it will still look of about 1 arcmin.

It can’t be magnified using telescope.

(c) Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about . from the earth. Calculate what size it will appear when seen through the same telescope.

Explanation:

.

At sun is seen as degree in diameter, and mars will be seen as degree in diameter.

At A.U, mars will be seen as degree in diameter. With 100 magnification mars will be seen as degree arcmin.

This is larger than resolution limit due to atmospheric fluctuations. Hence, it looks magnified.

44). Einstein’s mass - energy relation emerging out of his famous theory of relativity relates mass (m) to energy (E ) , where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in where ; the masses are measured in unified atomic mass unit (u) where

(a) Show that the energy equivalent of

Explanation: Since its energy equivalent is in SI units. When converted to eV and , it turns out to be

(b) A student writes the relation as . The teacher points out that the relation is dimensionally incorrect. Write the correct relation

Explanation: