List of top Physics Questions on Dimensional formulae and dimensional equations

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 : 

1. atoms are very small objects 
2. a jet plane moves with great speed 
3. the mass of Jupiter is very large 
4. the air inside this room contains a large number of molecules 
5. a proton is much more massive than an electron 
6. the speed of sound is much smaller than the speed of light.

A famous relation in physics relates ‘moving mass’ \(\text m\) to the ‘rest mass’ \(\text m_0\) of a particle in terms of its speed v and the speed of light, \(\text c\) . (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant \(\text c\). He writes : \(\text m\) = \(\frac{\text m_0}{(1-v^2)^{\frac{1}{2}}}\) . Guess where to put the missing \(\text c\).