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Q. 54.3( 44 Votes )

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?

Class 11th NCERT - Physics Part-I 2. Units and Measurements

Answer :

We know that speed of light in vacuum, c = 3 × 10⁸ m/s

Relation between speed & distance travelled

Distance travelled ‘x’ = speed × time taken ------- (1)

Here the value of time taken is given

t = 8 min 20 s = 500 s

So, x = s × t

x = c × t

Where c = speed of light

t = time taken

= 3 × 10⁸ ms^-1 × 500 m

= 1.5 × 10¹¹ m

So this is the distance between the sun and the earth.

We have to express the above distance value in terms of new units. In new units, the value of the speed of light is unity.

i.e, c = 1 unit

t = 500 s

Substituting the above values in equation (1)

Distance between sun & Earth x = c × t

= 1 unit × 500 s

= 500 new units

Distance between Sun & Earth = 500 new units

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PREVIOUSExplain 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:A. Atoms are very small objectsB. A jet plane moves with great speed.C. The mass of Jupiter is very large.D. The air inside this room contains a large number of molecules.E. A proton is much more massive than an electron.F. The speed of sound is much smaller than the speed of light.NEXTWhich of the following is the most precise device for measuring length:(a). A Vernier callipers with 20 divisions on the sliding scale(b). A screw gauge of pitch 1 mm and 100 divisions on the circular scale(c). An optical instrument that can measure length to within a wavelength of light?

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