QUESTIONS FOR SHORT ANSWER1)The metre is defined as the distance travelled by light in 1/299,792,458 second. Why didn't people choose some easier number such as 1/300,000,000 second? Why not 1 second?2) What are the dimensions of (a) volume of a cube of edge a(b) volume of a sphere of radius a(c) the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?3) 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 metre 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?4) If all the termsin an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?5) If two quantities have same dimensions, do they representsame physical content?6) It is desirable that the standards of units be easily available, invariable, indestructible and easily rproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are no?7) Suggest a way to measur : (a) the thickness of a sheet of paper, (b) the distance between the sun and the moon.

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by jafiya

2014-11-23T09:43:41+05:30

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1)
The meter was standardized much before the velocity of light was precisely determined.  Long back the length of a meter was determined and every where this standard is already in use. Like in tailor shops, carpenters, schools, books etc.  So, it is not possible to change the length of a meter.

It has been determined that light travels 299, 792, 458 meters/second experimentally and theoretically.  Speed of Light is supposed to be the most invariant of the physical quantities in the universe.  It does not change.  Other standards like length of a rod or bar will vary depending on temperature.  The measurement may depend on geographical location too.  So a meter is defined as  1/299, 792, 458 of distance travelled by light in a second.

2)
cube volume = a³   dimension = Length³    units = meter³  or cm³
sphere  volume = 4π/3 a³,   dimension = length³    units = meter³   or cm³

ratio = a³ / (4π/3 a³) = 3/4π

3)
If length of everything changes to twice, then the length of meter bar or measuring tape also becomes twice.  So it is not possible to detect the change.  Because even human beings, the buildings etc. will change proportionately.
If we make the hypothesis that speed of light is constant, then we can test the change of lengths in universe.  Then using our measurement techniques of time and length the speed of light will be found to be 1/2 of its original speed.
Clocks will show the same time as before. They will not change. Time is found as ratios of two physical quantities, so the doubling effect is cancelled.

4)
All the terms in an equation must have the same dimensions and same units for proper addition or subtraction or to equate them.  You have to convert all the terms in to one single unit.
You can write as   5 meters + 3 cm = 5, 030 mm
But to verify, compute you must convert them all into one unit, as in
5, 000 mm+ 30 mm = 5, 030 mm

5)
two physical quantities have same dimensions, but they can have different units.
5 meters,   5 cm,  5 mm  all have  dimension as Length. [ L ].  But different units and different magnitude values.

6)

foot - easily available.  it is not invariable..   it is not indestructible.  it is not easily reproducible, the length may change in time over years, as people grow and get diseases which can alter the length of foot.

7)

1. by intensity of light from sun directly and that of light reflected by Moon.
2. At the time of eclipse, we can find the distance between Earth and Sun and distance between Earth and Moon.  Then we subtract or add to get the distance.
3. using the lunar year, Earth's year  and distance between earth and moon.

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