If velocity of light c, Plank's constant h and gravitational ontant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

If momentum (p), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula

If Planck's cosntant (h) and speed of light in vaccum (c ) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?

Why length, mass and time are chosen as base quantities in mechanics?

Using mass (M), length (L) time (T) and current (A) as fundamental quantities, the dimension of permeability is

Agreat physicist of this century (RA.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close 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 can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants ?

Write down the dimensions of each of the following in terms of mass,length ,time and charge: modulus of rigiditty.

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.

In the expression P = E l^2 m^-5 G^-2 , E,m,l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.