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Chapter 2 Units and Measurements Solutions

Question - 31 : -

The farthest objects in our Universe discovered by modernastronomers are so distant that light emitted by them takes billions of yearsto reach the Earth. These objects (known as quasars) have many puzzlingfeatures, which have not yet been satisfactorily explained. What is thedistance in km of a quasar from which light takes 3.0 billion years to reachus?

Answer - 31 : -

Time taken by quasar light to reach Earth = 3 billion years

= 3 × 109 years

= 3 × 109 × 365 × 24 × 60 × 60 s

Speed of light = 3 × 108 m/s

Distance between the Earth and quasar

= (3 × 108) × (3 × 109 × 365 × 24 × 60× 60)

= 283824 × 1020 m

= 2.8 × 1022 km

Question - 32 : -

It is a well known fact that during a total solar eclipse the diskof the moon almost completely covers the disk of the Sun. From this fact andfrom the information you can gather from examples 2.3 and 2.4, determine theapproximate diameter of the moon.

Answer - 32 : -

The position of the Sun, Moon, and Earth during a lunar eclipse isshown in the given figure.

Distance of the Moon from the Earth = 3.84 × 108 m

Distance of the Sun from the Earth = 1.496 × 1011 m

Diameter of the Sun = 1.39 × 109 m

It can be observed that ΔTRS and ΔTPQ are similar. Hence, it canbe written as:

Hence, the diameter of the Moon is 3.57× 106 m.

Question - 33 : - A great physicist of this century (P.A.M. Dirac) lovedplaying with numerical values of Fundamental constants of nature. This led himto an interesting observation. Dirac found that from the basic constants ofatomic physics (c, e, mass of electron, mass of proton) andthe gravitational constant G, he could arrive at a number with thedimension of time. Further, it was a very large number, its magnitude beingclose to the present estimate on the age of the universe (~15 billion years).From the table of fundamental constants in this book, try to see if you too canconstruct this number (or any other interesting number you can think of). Ifits coincidence with the age of the universe were significant, what would thisimply for the constancy of fundamental constants?

Answer - 33 : -

One relation consists of some fundamental constants that give theage of the Universe by:

Where,

t = Age of Universe

e = Charge of electrons = 1.6 ×10–19 C

 = Absolute permittivity

= Mass of protons = 1.67 × 10–27 kg

= Mass of electrons = 9.1 × 10–31 kg

c = Speed of light = 3 × 108 m/s

G = Universal gravitational constant = 6.67 × 1011 Nm2 kg–2

Also,Nm2/C2

Substituting these values in the equation, we get

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