Short Answers:

1) The speed of light in vacuum is 299,792,458 m/s. Then time taken by light to cover a distance of 1 metre in vacuum = 1 / 299,792,458 s.

Hence, the metre is defined as the distance travelled by light in 1 / 299,792,458 s.

As 300,000,000 m/s is an approximate speed of light in vacuum, it cannot be used to define the metre.

The distance travelled by light in one second is 299,792,458 m. This is a large quantity and cannot be used as a base unit. So, the metre is not defined in terms of second.

2) (a) Volume of a cube of edge a, V = a

^{3}

i.e., [V] = L L L = L

^{3}

(b) Volume of a sphere of radius a, V = (4/3)ΠR

^{3}

i.e., [V] = L L L = L

^{3}

(c) M

^{0}L

^{0}T

^{0}, a dimensionless quantity.

3) No, Yes, No

The validity of this statement cannot be tested by measuring sizes with a metre stick, because the size of the metre stick has also got doubled overnight. Yes, it can be verified by using the fact that speed of light is a universal constant and has not changed.

If the linear size of everything in the universe is doubled and all the clocks in the universe starts running at half the speed, then we cannot test the validity of this statement by any method. (See example)

After clock becomes slow, when 1 hr passes in clock, 2 hours pass in reality.

Originally, distance travelled by light,

*l*= c.t

But, in new clock time, distance travelled, 2

*l*= c.2t

∴

*l*= ct.

4) Yes, if all the terms in an equation have the same units, it is necessary that they have the same dimension.

No, if all the terms in an equation have the same dimensions, it is not necessary that they have the same unit.

e.g., ω = 2Π

*f*

Both have dimensions [T

^{-1}]

Π has unit rad/sec but frequency has hertz.

5) No, even if two quantities have the same dimensions, they may represent different physical contents.

Example: Torque and energy have the same dimension, but they represent different physical contents.

6) Features present – Easily available

Features absent – Invariable, Indestructible and easily reproducible

7) a) Measure thickness of 100 pages together and divide the measured value by 100.

b) The distance between the Sun and the Moon can be measured by using Pythagoras theorem when the Earth makes an angle of 90

^{o}with the Sun and the Moon. We already know the distances from the Sun to the Earth and from the Earth to the Moon. However, these distances keep on changing due to the revolution of the Moon around the Earth and the revolution of the Earth around the Sun.

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