Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a meter stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?
o If length of everything changes to twice then the length of meter bar or measuring tape also because twice so it not possible to detect the change because even human beings the building etc. will change proportionally
o if we make the hypothesis that speed of light is constant, then we can test the change of length in universe
o Then using our measurement techniques of time and length the speed of light will be found to be 1/2 of its original speed
o Clock will show the same time before they will not change time is found as ratio of two physical quantities so the doubling effect is cancelled
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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
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Physics - Exemplar