Unit 1: Measurements — Short Questions

Base units are fundamental units that are independent of other units.
Examples: meter (length), kilogram (mass), and second (time) etc.
Derived units are combinations of base units.
Examples: newton (N = kgm/s² for force) and joule (J = kg·m²/s² for energy) etc.

i. The result should have the same number of significant figures as the input value with the least significant figures.
ii. The result should have the same number of decimal places as the input value with the least decimal places.

The Vernier scale slides along the main scale and has divisions slightly smaller than the main scale.
The smallest measurement that can be taken by using Vernier Calipers is called its least count, calculated as:
[L.C. = 1 main scale division – Vernier scale division]
L.C = 0.01 cm or 0.1mm

(a) (1.437 × 10²)
(b) (2.064 × 10⁴)

(a) (580 × 10² g = 58,000 g = 58 kg)
(b) .45 × 10⁻⁵ s = 4.5 × 10⁻⁶ s = 4.5 us)

Dimensions of kinetic energy are derived as; K.E = 1/2 mv² = [M][LT⁻¹]²
[M][L²T⁻²] = [ML²T⁻²]
Here,
[M] = mass, [L] = length, [T] = time.

i. 2 (all non-zero digits are significant).
ii. 4 (leading zeros are not significant).
iii. 6 (zeros between or after decimals are significant).
iv. 4 (trailing zeros with a decimal are significant).

(i) As E = hf ⟹ h = E/f
[h] = [E]/[f]
Dimension of energy (E) = [ML²T⁻²]
Dimension of frequency (f) = [T⁻¹]
[h] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]
(ii) ω = ΔΘ/t ⟹ = [1/T] = [T⁻¹] ∴ θ is dimensionless, s.
Angular velocity (ω) : Dimensions are ([T⁻¹]) (unit: rad/s, where radian is dimensionless).

Force = mass x acceleration
[F] = [M] × [a] = [M][LT⁻²] = [MLT⁻²]
[P] = [F]/[A] = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]

All the accurately known digits and first doubtful digit are called significant figures.

The representation of a value in the power of ten with only one non-zero number to the left of decimal, e.g. 0.0023=2.3 × 10⁻³.

It is a standard which is used for the measurement of a physical quantity and in terms of which laws of physics are expressed.

The quantities which can be measured physically and in terms of which laws of physics are expressed are known as physical quantities.

In order to check the correctness of equation, the dimensions of the quantities on both sides of the equation should be same, irrespective of the form of the formula, is called principle of homogeneity of dimensions.

Following are the two uses of dimensional analysis:
(i) Checking the correctness of mathematical equation.
(ii) Deriving a possible formula of the physical quantity.

Volume of cube of edge length "L":
V = L³ = (2.25)³ % uncertainty in L³ =
3 × [0.01/2.25 × 100] = 13.2%

The term used for multiples and submultiples for various units are called prefixes. e.ge. 5 × 10⁻⁶ s, 10⁻⁶ is a prefix and it also called micro.

It is the distance covered by light in one year. It is a unit of distance employed in Astronomy 1 light year = 9.5 x 10¹⁵m.

As S = ct
One light year = 3 × 10⁸ m/sec × 1 year
One light year = 3 × 10⁸ × 356 × 24 × 3600m
One light year = 9.5 × 10¹⁵ m.

(i) I = F × t
[I] = [MLT⁻²][T]
[I] = [MLT⁻¹]
(ii) Also p = mv
[p] = [M][V]
[p] = [MLT⁻¹]
= [M][LT⁻¹]
= [MLT⁻¹]