In defining the standard of length we have to specify the temperature at which the measurement should be made. Are we justified in calling length a fundamental quantity if an other physical quantity, temperature has to be specified in choosing a standard?

Comment on statement : "To define a physical quantity for which no method of measurment is given or known has no meaning."

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of and see if we can get a quantity with the dimensions of length that is roughly equal to the known of an atom (~ 10^ -10 m).- Construct a quantity with the dimensions of length from the fundamental constants e, m_e , and c. Determine its numerical value.

classically an electron can be in any orbit around nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? Thequestion had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as followswith the basic constants of nature e, me, c and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10 m).- You will find that the length obtained above is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for else h had already made its appearance elsewhere. Bohr lay in recognising that h, m_e , and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remains constant. If alpa_(iron = 1.2 xx 10^-5 //K and alpha_(brass = 1.8 xx 10^-5//K , what should we take as length of each strip?

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.

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (4, 3).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (3, 4).

Explain this statement clearly: "To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparision". In view of this, reframe the following statements wherever necessary: The mass of Jupiter is very large

Explain this statement clearly :- " To call a dimensional quantity large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary :- the speed of sound is much smaller than the speed of light.

Explain this statement clearly :- “To call a dimensional quantity large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary :- atoms are very small objects