Unit of Length: SI and Other units, Conversion and Important Questions

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Unit of Length: Length is defined as the measurement of something from one end to the other. The SI unit of length is m, but there are many other units of length in other systems of measurement. Let us look at the various units of length that are used around the world.

Table of Content

Length
SI Unit of Length
Other Units of Length
Conversion of Units of Length
Scientific Unit of Length
Things to Remember
Sample Questions

Length

Length is the measurement of something from one end to the other. In other words, the length defines how long something is. It is defined as a quantity with dimension distance in the International System of Quantities.

The length of the path travelled by light in a vacuum within 1/299792458 seconds.

Units and Measurements Video Lecture

Metric System unit of Length

Unit

Any physical amount is measured by comparing it to a basic, arbitrarily chosen and internationally accepted reference standard known as a unit.

Different systems of units for measurement

CGS system include centimetre, gram, and second
FPS system include foot, pound, and second
MKS system include metre, kilogram, and second

The Système Internationale' Unites (French for International System of Units), abbreviated as SI, is the international measurement system which is currently in use. The SI was established and recommended by the General Conference on Weights and Measures in 1971 for international use in scientific, technical, industrial, and commercial activities, with a consistent scheme of symbols, units, and abbreviations.

Unit of Length

The metre is the base unit for length in the International System of Units (SI). It is abbreviated as m.

This is possible when the length is given in appropriate units, such as 2 metres or 200 centimetres for a table, 15 metres for a string, and so on.

Other Units of Length

10 millimeters (mm)	1 centimeter (cm)
10 centimeters	1 decimeter (d)
10 decimeters	1 meter (m)
10 meters	1 decameter (da)
10 decameter	1 hectometer (h)
10 hectometers	1 kilometers (km)

Conversion of Units of Length

Units	Conversion
Km to Cm	1 km = 100000 cm
Km to M	1 km = 1000m
Cm to m	1 cm = 0.01m
M to mm	1 m = 1000 mm
Cm to mm	1cm = 10 mm

Scientific Units of Length

Astronomical Unit: The mean distance between the Earth and the Sun is measured in astronomical units. It is used to calculate orbits and trajectories throughout the Solar System.

1 UA = 149,597,871 km

Light Year: The distance travelled by light in one average solar year is measured in light-years. It is used to measure extraordinarily long distances in astronomy.

1 light-year = 9,461,000,000,000 km

Parsec: A parsec is an astronomical unit of measurement that equals the distance between the earth and an astronomical object with a one-second parallax angle.

1 parsec = 30,857,000,000,000 km

Things to Remember Based on Unit of Length

Length is the measurement of something from one end to the other.
CGS system- centimetre, gram, and second
FPS system- foot, pound, and second
MKS system- metre, kilogram, and second
Metre is the SI unit for length. It is abbreviated as m.
The mean distance between the Earth and the Sun is measured in astronomical units. 1 UA = 149,597,871 km
The distance travelled by light in one average solar year is measured in light-years. 1 light-year = 9,461,000,000,000 km
A parsec is an astronomical unit of measurement. 1 parsec = 30,857,000,000,000 km

Important Questions Based on Unit of Length

Ques: What is the difference between A^o and A.U.? (1 Mark)

Ans: A^o and A.U. both are units of length. The major difference between both of the units is- 1A^o = 10^-10m and 1 A.U. = 1.496 x 10¹¹m.

Ques: Do A.U. and A^o represents the same magnitudes of length? (1 Mark)

Ans: No, A.U. and Ao do not represent the same magnitudes of length 1 A.U. = 1.496 x 10¹¹m and 1 A^o= 10^-10 m.

Ques: Suggest a length corresponding to each of the following order of length:

(a) 10^-4 m

(b) 10^-9 m

(c) 10⁴ m

(d) 10⁷ m

(e) 10⁹ m. (2 Marks)

Ans: (a) Size of the atomic nucleus

(b)Size of the oil molecule

(c) Height of Mount Everest

(d) Radius of Earth

(e) The radius of the Sun.

Ques: Define dimensions of a physical quantity. (2 Marks)

Ans: Dimensions of a physical quantity are defined as the powers to which the fundamental units of mass, length, and time have to be raised to obtain its units. For Example- The unit of area is [M⁰ L² T⁰]. Thus its dimensions are 1 zero in mass, 2 in length, and zero in time.

Ques: Define standard meter. (2 Marks)

Ans: Standard meter is equal to exactly 1650763.73 wavelengths of orange-red light emitted in vacuum by krypton-86 atom i.e. kr⁸⁶.

e. 1 metre = 16,50,763.73 wavelengths.

It is also defined as the distance traveled by light in 1/299792458 seconds.

Here, the exact value of the velocity of light is 299792458 ms^-1.

Practically, c = 2.9 × 10⁸ ms^-1 = 3.0 × 10⁸ ms^-1.

Ques: Define one parsec. (2 Marks)

Ans: One parsec is defined as the distance at which an arc of length equal to one astronomical unit subtends an angle of one second at a point.

Ques: The unit of length convenient on the atomic scale is known as an angstrom and is denoted by A^o (1A^o = 10^-10 m). The size of a hydrogen atom is about 0.5 A^o what is the total atomic volume in m³ of a mole of hydrogen atoms? (3 Marks)

Ans: Radius of hydrogen atom, r = 0.5 A^o = 0.5 x 10^-10 m =

Volume of hydrogen atom =4/3π r³

= 4/3 x 22/7 x (0.5x 10^-10 )³

= 0.524 x 10^-30m³

1 mole of hydrogen has 6.023 x 10²³ hydrogen atoms.

∴ Volume of 1 mole of hydrogen atoms = 6.023 x 10²3 x 0.524 x 10^-30

= 3.16 x 10^-7 m³

Ques: Convert the following- (3 Marks)

5 cm to mm

10 m to cm

15 km to m

Ans: a) 5 cm to mm –

We know, 1 cm=10 mm

5cm = 5 * 10 = 50 mm.

10m to cm-

We know, 1m = 100 cm

10m = 10 * 100 = 1000cm .

15km to m

We know, 1 km = 1000m

15km = 15 * 1000 = 15000m

Ques: Convert the following -

52.8 cm to mm

68.7 m to cm

6.26 m to mm

8.75 km to mm (4 Marks)

Ans: a) 52.8 cm to mm
1 cm = 10 mm
52.8 cm = 52.8 * 10 = 528mm

68.7 m to cm
1m = 100 cm
7 m = 68.7 * 100 = 6870 cm

6.26 m to mm
1 m = 10 mm
26 m = 6.26 * 10 = 62.6 mm.

8.75 km to mm
1 km = 1000 m
75 km = 8.75 * 1000 = 8750m
1m = 100 cm
8750 m = 8750 * 100= 875000 cm
1 cm = 10 mm
875000 cm = 875000 * 10 = 8750000 mm

CBSE CLASS XII Related Questions

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).
View Solution
2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.
View Solution
3.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:
- attract with a force \( \frac{F}{2} \)
- repel with a force \( \frac{F}{2} \)
- repel with a force \( F \)
- attract with a force \( F \)
View Solution
4.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]
View Solution
5.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))
View Solution
6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.
View Solution

View All

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Unit of Length: SI and Other units, Conversion and Important Questions

Length

Units and Measurements Video Lecture

Unit

Different systems of units for measurement

Unit of Length

Other Units of Length

Conversion of Units of Length

Scientific Units of Length

Things to Remember Based on Unit of Length

Important Questions Based on Unit of Length

CBSE CLASS XII Related Questions

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

5.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

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Unit of Length: SI and Other units, Conversion and Important Questions

Length

Units and Measurements Video Lecture

Unit

Different systems of units for measurement

Unit of Length

Other Units of Length

Conversion of Units of Length

Scientific Units of Length

Things to Remember Based on Unit of Length

Important Questions Based on Unit of Length

CBSE CLASS XII Related Questions

1.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

5.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

5.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.