### Units and Measurements Important Extra Questions Very Short Answer Type

Question 1.

If the size of the atom were enlarged to the tip of the sharp pin, how large would the height of Mount Everest be?

Answer:

10^{10} m.

Question 2.

What does the LASER mean?

Answer:

It stands for Light Amplification by Stimulated Emission of Radiation.

Question 3.

If the Universe were shrunk to the size of the Earth, how large would the Earth be on this scale?

Answer:

1o^{-11} m (size of an atom.).

Question 4.

A research worker takes 100 careful readings in an experiment. If he repeats the same experiment by taking 400 readings, then by what factor will the probable error be reduced?

Answer:

By a factor of 4.

Question 5.

What is the number of significant figures in 0.06070?

Answer:

4.

Question 6.

Which of the following reading is most accurate?

(a) 7000m,

(b) 7 × 10^{2} m,

(c) 7 × 10^{3} m

Answer:

(a) i.e. 7000 m.

Question 7.

The density of a cube is calculated by measuring the length of one side and its mass. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then what is the maximum possible error in the measurement of density?

Answer:

3% + 3 × 2% = 9%.

Question 8.

The mass of a body as measured by two students is given as 1.2 kg and 1.23 kg. Which of the two is more accurate and why?

Answer:

The second measurement is more accurate as it has been made to the second decimal point.

Question 9.

Do the inertial and gravitational masses of ordinary objects differ in magnitude?

Answer:

No.

Question 10.

Are S.I. units Coherent? Why?

Answer:

Yes, because all the derived units in this system can be obtained by multiplying or dividing a certain set of basic units.

Question 11.

Do A.U. And Å represents the same magnitudes of distance?

Answer:

No, 1 A.U. = 1.496 × 10^{11} m and 1 Å = 10^{10} m.

Question 12.

What does SONAR stand for?

Answer:

It stands for Sound Navigation and Ranging.

Question 14.

Which is the most accurate clock?

Answer:

Cesium atomic clock.

Question 15.

Write the S.I. units of the following physical quantities:

(a) Luminous intensity

Answer:

Candela (cd)

(b) Temperature

Answer:

Kelvin (K)

(c) Electric current

Answer:

Ampere (A)

(d) Amount of substance

Answer:

Mole (mol)

(e) Plane angle

Answer:

Radian (rd)

(f) Solid angle

Answer:

Steradian (sr)

(g) Pressure.

Answer:

Nm-2 = pascal (pa).

Question 16.

What is the difference between mN, Nm, and nm?

Answer:

- mN means.milli-newton, 1 mN = 10
^{-3}N. - Nm means newton-meter, 1 Nm = 1 J
- nm means namometer, 1 nm = 10
^{-9}m.

Question 17.

If x = a + bt + ct^{2} where x is in meter and t in seconds, what is the unit of c?

Answer:

The unit on the left-hand side is a meter so the units of ct^{2} should also be a meter. Since t^{2} has units of s^{2}, so the unit of c is ms^{-2}

Question 18.

Will the dimensions of a physical quantity be the same, whatever be the units in which it is measured? Why?

Answer:

Yes, the dimensions don’t depend on the system of units chosen.

Question 19.

Write the dimensions of:

(i) gravitational constant

Answer:

[M^{-1} L^{3} T^{2}]

(ii) Plank’s constant

Answer:

[M L^{2} T^{-1}]

(iii) torque

Answer:

[M L^{2} T^{2}]

(iv) surface tension

Answer:

[M L^{0} T^{-2}]

(v) angular momentum.

Answer:

[M L^{2} T^{-1}]

Question 20.

Name at least two physical quantities each having dimensions:

(a) [M L^{-1} T^{-2}]

Answer:

Pressure and stress,

(b) [M L^{2} T^{-1}]

Answer:

Plank’s constant and angular momentum.

Question 21.

State the principle of homogeneity of dimensions?

Answer:

It states that the dimensions of each term on both sides of an equation are the same.

Question 22.

Which are the main types of errors in a physical measurement?

Answer:

Main errors are systematic error, random error, gross error, relative error, and percentage error.

Question 23.

Which one is large, the number of microseconds in a second or the number of seconds in a year?

The number of seconds in a year = 10^{7}s and the number of microseconds in a second = 10^{6}μs. So the number of seconds in a year is larger than microseconds in a second.

Question 24.

Do significant figures change if the physical quantity is measured in different systems of units?

Answer:

No, significant figures don’t depend on the system of units. e.s. 250 g = 2.50 × 10^{-1} kg.

Both have 3 significant figures.

Question 25.

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

(a) 10^{-4} m

Answer:

Size of the atomic nucleus

(b) 10^{-9} m

Answer:

Size of the oil molecule

(c) 10^{4} m

Answer:

Height of Mount Everest

(d) 10^{7} m

Answer:

Radius of Earth

(e) 10^{9} m.

Answer:

The radius of Sun.

Question 26.

What do you understand by the following?

(a) Century

Answer:

It is the largést unit of time, 1 century = 100 years.

(b) Shake

Answer:

It is the smallest unit of time, 1 shake = 10^{-8}s.

(c) Lunar month

Answer:

It is the time taken by the moon to complete one revolution around the Earth, 1 lunar month = 27.3 days.

(d) Leap year

Answer:

A year that is divisible by four and in which the month of February is of 29 days is called a leap year.

(e) Tropical year.

Answer:

The year in which the total solar eclipse takes place is called a tropical year.

Question 29.

What do you mean by the term measurement?

Answer:

Measurement means the comparison of a physical quantity with its unit to find out how many times the unit is contained in the given physical quantity.

Question 30.

Sort out the incorrect representation of units and write them

(i) m/sec

Answer:

ms^{-1}

(ii) Newton

Answer:

newton

(iii) kelvin

Answer:

kelvin

(iv) m.m.

Answer:

mm

(v) Jk^{-1}

Answer:

JK^{-1}

(vi) kg/m^{3}

Answer:

kgm^{-3}

(vii) wH

Answer:

Wh

(viii) gms^{-2}

Answer:

gs2

(ix) length = 5M

Answer:

length = 5 m

(x) B = 4g (B = magnetic field intensity).

Answer:

B = 4G

Question 31.

Define light year.

Answer:

It is defined as the distance traveled by light in one year.

1 L.Y. (ly) = 3 × 10^{8} ms^{-1} × 365 × 24 × 60 × 60s ≈ 9.46 × 10^{15} m.

Question 32.

Define Astronomical distance.

Answer:

It is defined as the distance between the Earth and Sun.

1 A.U. = 1.496 × 10^{11} m~ 1.5 × 10^{11} m.

Question 33.

What is the limit of

(i) accuracy

Answer:

The least count of the measuring instrument is the limit of accuracy with which a physical quantity can be measured.

(ii) error?

Answer:

The error in measurement is taken equal to half the least count.

Question 34.

What do you mean by ‘Order of magnitude’?

Answer:

Order of magnitude is defined as the approximation to the nearest power of 10 used to express the magnitude of a physical quantity under consideration, e.g.

- The order of magnitude of the time interval of 1.2 × 10
^{-6}s is -6. - The order of magnitude of the distance of 4.5 × 10
^{6}is +6.

Question 35.

Find the order of magnitude of a light-year.

Answer:

I light year = 9.46 × 10^{15} m ≈ 10^{16}m

∴ The order of magnitude of light-year is +16.

Question 36.

Derive the dimensional formula of:

(a) Angular velocity

Answer:

Angular velocity = Angle / Time =1 /T = [M^{0} L^{0} T^{-1}]

(b) Angular momentum

Answer:

Angular momentum = momentot inertia × Angular velocity

= mass x (radius of rotalion)^{2} (Time)^{-1}

= [M L^{2} T^{-1}].

Question 37.

Derive the dimensional formula of:

(a) Impulse

Answer:

Impulse = Force x Time

= [M L T^{-2}][T]

= [M L^{2} T^{-1}].

Question 42.

Define the dimensional formula of a physical quantity.

Answer:

It is defined as an expression that shows which of the fundamental units and with what powers appear into the derived unit of a physical quantity.

e.g. dimensional formula of force is [M^{1 }L^{1} T^{2}].

Question 43.

Define dimensional equation of a physical quantity.

Answer:

It is defined as the equation obtained by equating the symbol of a physical quantity with its dimensional formula, e.g. [F] = [M L T^{-2}] is the dimensional equation of force.

Question 44.

Define one kilogram.

Answer:

It is the mass of platinum-iridium cylinder (90% Pt + 10% Ir) having its diameter equal to its height (both equal to 3.9 cm) kept in the International Bureau of Weights and Measures of Sevres near Paris.

Question 45.

Define one second.

Answer:

It is defined as the time interval occupied by 9, 192, 631, 770 vibrations corresponding to the transition between two hyperfine levels of cesium -133 (Cs^{133}) atom in the ground state.

Question 46.

Define one ampere.

Answer:

It is defined as that constant current which when flowing through two parallel, straight conductors of the infinite length of negligible cross-section held one meter apart in a vacuum produces a force of 2 × 10^{-7} N/m between them.

Question 47.

Define Kelvin.

Answer:

It is defined as 1/273.16 fraction of the thermodynamic temperature at the triple point of water.

Question 48.

Define radian.

Answer:

It is defined as the angle made at the center of a circle by an arc of length equal to the radius of the circle.

Question 49.

Define steradian.

Answer:

It is defined as the solid angle made at the center of a sphere by an area cut from its surface whose area is equal to the square of the radius of the sphere.

Question 50.

Define one mole.

Answer:

It is defined as the amount of substance that contains the same number of elementary units {i.e. atoms) as there are atoms in 0.012 kg of carbon-12.

Question 51.

Define standard meter.

Answer:

It is defined to be equal to exactly 1650763.73 wavelengths of orange-red light emitted in vacuum by krypton-86 atom i.e. kr^{86}.

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

Or

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

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

For all practical purposes, c = 2.9 × 10^{8} ms^{-1} = 3.0 × 10^{8} ms^{-1}.

### Units and Measurements Important Extra Questions Short Answer Type

Question 1.

If the size of a nucleus is scaled up to the tip of a sharp pin, what roughly is the size of an atom?

Answer:

The size of a nucleus is in the range of 10^{-15} m to 10^{-14 }m. The tip of a sharp pain may be taken to be in the range of 1o^{-5} m to 10^{-4} m. Thus we are scaling up the size of the nucleus by a factor of 10^{-5}/10^{-15 }= 10^{10}. An atom roughly of size 10^{-10} m will be scaled up to a rough size of 10^{-10} × 10^{10} = 1 m. Thusanucleus in an átom is as small in size as the tip of a sharp pin placed at the center of a sphere of radius about a meter.

Question 2.

(a) What do you mean by physical quantity?

Answer:

It is defined as a quantity that can be measured, e.g. mass, length, time, etc.

(b) What do you understand by:

(i) Fundamental physical quantities?

Answer:

They are defined as those quantities which cannot be expressed in terms of other quantities and are independent of each other, e.g. mass, length, time.

(ii) Derived physical quantities?

Answer:

They are defined as the quantities which can be expressed in terms of fundamental quantities, e.g. velocity, acceleration, density, pressure, etc.

Question 3.

(a) Define the unit of a physical quantity.

Answer:

It is defined as the reference standard used to measure a physical quantity.

(b) Define:

(i) Fundamental units.

Answer:

They are defined as the units of fundamental quantities. They are independent of each other and are expressed by writing the letter of the fundamental quantity in a parenthesis.

e.g. Fundamental units of mass, length and time are [M], [L], [T] respectively.

(ii) Derived units.

Answer:

They are defined as those units which can be derived from fundamental units. They are expressed by writing the symbol of a derived quantity in a parenthesis.

e.g. D.U. of velocity = [u]

acceleration = [a]

pressure = [P]

work = [W] and so on.

Question 4.

Define one Candela.

Answer:

It is defined as the luminous intensity in a perpendicular direction of a surface of 1/600,000 square meter area of a black body at a temperature of freezing platinum (1773°C) under a pressure of 101,325 N/m^{2}.

It is the S.I. unit of luminous intensity.

Question 5.

What is the advantage of choosing wavelength of light radiation as standard of length?

Answer:

- It can be easily made available in any standard laboratory as Krypton is available everywhere.
- It is well defined and does not change with temperature, time, place or pressure, etc.
- It is invariable.
- It increases the accuracy of the measurement of length (1 part in 10
^{9}).

Question 6.

Which type of phenomenon can be used as a measure of time? Give two examples of it.

Answer:

Any phenomenon that repeats itself regularly at equal intervals of time can be used to measure time.

The examples are:

- Rotation of earth – the time interval for one complete rotation is called a day.
- Oscillations of a pendulum.