Test: Measurement of Length (NCERT) - NEET MCQ

Fathom is a unit of length equal to six feet. It is used to measure depth of sea. 

Angstrom, femi and parsec are the units of length whereas barn is the unit of nuclear cross-section.

A. Distance between earth and sun - Light year
B. Interatomic distance in a solid - Angstrom
C. Size of a nucleus - Fermi
D. Wavelength of infrared laser - Micron 

1 mm = 10^-3m; 1 Å = 10^-10m; 1 fm = 10^-15m
Among the given units fermi is the smallest unit. 

Vernier callipers, screw gauge and spherometer are used for the measurement of length whereas atomic clock is used for the measurement of time.

Here, Speed of light in vacuum, c = 1 new unit of length s^-1. 
Time taken by light of sun to reach the earth
t = 8 min and 20 seconds = (8 x 60 + 20) s = 500 s
∴ Distance between the sun and the earth
S = ct = 1 new unit of length s^-1 x 500 s
= 500 new unit of length

Topic in NCERT: Units and measurement

Line in NCERT: "1.5 a new unit of length is chosen such that the speed of light in 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?"

Light year is the distance travelled by light in free space in one year.

1 light year = 9.46 x 10¹⁵ m
(Distance travelled by light in 1 year)

Alpha centauri is 4.29 light years away from the earth.

A laser is a source of very intense, monochromatic and undirectional beam of light .These properties of laser light can be exploited to measure long distances.

From figure,

∴ Diameter of the earth as seen from the moon is about 2^∘.

Here,
Distance of the sun from the earth, d = 1.496 × 10¹¹m
Suns angular diameter, α = 192′′
∵ 1′′ = 4.85 × 10⁻⁶ rad
∴ α = 1920 × 4.85 × 10⁻⁶ rad
= 9.31 × 10⁻³ rad
Suns diameter, D = αd
D = (9.31 × 10⁻³)(1.496 × 10¹¹)m
= 1.39 × 10⁹m

Here, θ = π/6, r = 30 cm 

The order of magnitude of the diameter of the earth is 7.

Topic in NCERT: Units and measurement

Line in NCERT: "the diameter of the earth (1.28×10^7m) is of the order of 10^7m with the order of magnitude 7."

The isotope Kr⁸⁶ was historically used as a standard for defining the meter. The number of wavelengths of Kr⁸⁶ in one meter is 1,650,763.73.

Volume occupied by 1 mole of an ideal gas at STP is known as molar volume.
∴ Molar volume = 22.4 litre = 22.4 x 10^-3 m³  
Radius of hydrogen atom is r = 0.5 Å = 0.5 x 10^-10 m


= 3.15 x 10^-7 m³ 
Their corresponding ratio is

Topic in NCERT: Significant figures

Line in NCERT: "the size of a hydrogen atom is about 0.5 å. what is the total atomic volume in m³ of a mole of hydrogen atoms?"

1 micron = 10^-6 m
∵ 10^-6 m space is occupied by 1 bacteria.
∴ 1 m space will be occupied by 
10⁶  bacteria = 1 million bacteria 

1 AU  = 1.496 x 10¹¹ m = 1.496 x 10⁸ km

Radius of the atom, R_a = 1 Å = 10^-10 m
Volume of the atom,

Radius of the nucleus, R_n = 1 fermi = 10⁻¹⁵m

Volume of the nucleus,

Their corresponding ratio is 

Given:
Pitch = 0.5 mm
Circular scale divisions = 50
Main scale reading = 0.5 mm
Zero error = -5 × 0.01 mm

We know that:
Least count (LC) = (Pitch) / (Circular scale divisions)
LC = 0.5 / 50 = 0.01 mm

Negative zero error = -5 × 0.01 mm = -0.05 mm

The measured value is:
Measured value = 0.5 mm + 25 × 0.01 - (-0.05) mm = 0.8 mm