Measurement/Unit Archives

31. Which one of the following is NOT a unit of ‘Pressure’?

Which one of the following is NOT a unit of ‘Pressure’?

Bar

Atmosphere

N/m²

N/m

This question was previously asked in

UPSC Geoscientist – 2021

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Pressure is defined as Force per unit Area (P = F/A). The unit of force is Newton (N) and the unit of area is square meter (m²), so the SI unit of pressure is N/m², also known as Pascal (Pa).
Looking at the options:
A) Bar is a unit of pressure (1 bar = 10⁵ Pa).
B) Atmosphere (atm) is a unit of pressure (1 atm ≈ 1.013 × 10⁵ Pa).
C) N/m² is the SI unit of pressure (Pascal).
D) N/m is a unit of force per unit length, which can represent surface tension or linear force density, but NOT pressure.

Pressure is force distributed over an area. Its units reflect this (Force/Area). Common units include Pascal (Pa), N/m², Bar, Atmosphere, psi (pounds per square inch), mmHg (millimeters of mercury), etc.

N/m is the unit of surface tension, which is the force acting per unit length along the surface of a liquid.

32. Which one of the following is NOT the correct unit of ‘power’?

Which one of the following is NOT the correct unit of ‘power’?

Joule / second

(Newton-metre) / second

Watt

Newton / metre

This question was previously asked in

UPSC Geoscientist – 2021

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Newton/metre (N/m) is NOT a correct unit of ‘power’.

Power is defined as the rate of doing work or transferring energy. Its standard unit in the SI system is the Watt (W).

Work is Force x Distance, measured in Joules (J) or Newton-metres (N.m). Power = Work/Time. So, Joule/second (J/s) and (Newton-metre)/second (N.m/s) are equivalent units of power. Watt (W) is defined as 1 Joule per second. Newton/metre (N/m) is a unit typically associated with force per unit length or surface tension.

33. Which one of the following is NOT a unit of magnetic field strength?

Which one of the following is NOT a unit of magnetic field strength?

Tesla

Gauss

Ampere - metre

Ampere/metre

This question was previously asked in

UPSC Geoscientist – 2020

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Ampere – metre (A·m) is NOT a unit of magnetic field strength.

Magnetic field strength can refer to magnetic flux density (B), measured in Tesla (T) or Gauss (G), or magnetic field intensity (H), measured in Amperes per metre (A/m). Ampere – metre (A·m) is the unit for magnetic dipole moment.

Tesla (T) is the SI unit for magnetic flux density (B). Gauss (G) is the CGS unit for magnetic flux density (1 T = 10^4 G). Ampere/metre (A/m) is the SI unit for magnetic field intensity (H). Magnetic field strength (H) and magnetic flux density (B) are related by the magnetic permeability of the medium ($B = \mu H$). Magnetic dipole moment (m) is a measure of the magnetic strength and orientation of a magnet or magnetic source.

34. Which one of the following physical quantities has the same dimensions

Which one of the following physical quantities has the same dimensions as that of Planck’s constant h?

Linear momentum

Angular momentum

Force

Potential energy

This question was previously asked in

UPSC CDS-2 – 2016

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The physical quantity that has the same dimensions as Planck’s constant (h) is angular momentum.

– Planck’s constant (h) relates the energy (E) of a photon to its frequency (ν) by the equation E = hν. The dimensions of E are [ML²T⁻²] and the dimensions of ν are [T⁻¹]. Therefore, the dimensions of h are [E/ν] = [ML²T⁻²] / [T⁻¹] = [ML²T⁻¹].
– Let’s check the dimensions of the given options:
– Linear momentum (p = mv): [M] * [LT⁻¹] = [MLT⁻¹].
– Angular momentum (L = Iω or L = rp): [Moment of inertia * Angular velocity] or [Radius * Linear momentum]. Dimensions are [ML²] * [T⁻¹] or [L] * [MLT⁻¹] = [ML²T⁻¹].
– Force (F = ma): [M] * [LT⁻²] = [MLT⁻²].
– Potential energy (e.g., mgh): [M] * [LT⁻²] * [L] = [ML²T⁻²].
– Comparing the dimensions, angular momentum [ML²T⁻¹] has the same dimensions as Planck’s constant [ML²T⁻¹].

In quantum mechanics, angular momentum is quantized in units of Planck’s reduced constant (ħ = h/2π), which has the same dimensions as h. This dimensional equivalence is not a coincidence but reflects a fundamental connection between energy, frequency, and angular momentum in quantum physics.

35. The pressure exerted by a 760 mm column of mercury at 0 °C is known a

The pressure exerted by a 760 mm column of mercury at 0 °C is known as

1 pascal

1 atmosphere

1 bar

1 poise

This question was previously asked in

UPSC CDS-2 – 2016

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The pressure exerted by a 760 mm column of mercury at 0 °C under standard gravity is known as 1 atmosphere.

– Standard atmospheric pressure is defined as the pressure that supports a column of mercury exactly 760 millimeters (or 76 cm or 29.92 inches) high at 0 °C at sea level and standard gravitational acceleration.
– This pressure is internationally defined as 1 standard atmosphere (atm).
– 1 atm is equivalent to 101,325 Pascals (Pa), which is the SI unit of pressure.
– 1 bar is another unit of pressure, equal to 100,000 Pa, which is slightly less than 1 atm.
– Pascal is the SI unit of pressure (N/m²).
– Poise is a unit of dynamic viscosity.

The height of the mercury column is directly proportional to the atmospheric pressure, as demonstrated by Torricelli’s experiment. This measurement is used in barometers to indicate atmospheric pressure.

36. The size of particles being studied in ‘nano-technology’ is about

The size of particles being studied in ‘nano-technology’ is about

1 Å – 10 nm

1 – 100 nm

1 – 50 µ

1 mm – 10 mm

This question was previously asked in

UPSC CDS-1 – 2021

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Nanotechnology is broadly defined as the understanding, manipulation, and control of matter at the nanoscale, typically ranging from approximately 1 to 100 nanometers (nm).

A nanometer (nm) is one billionth of a meter (10⁻⁹ m). The 1 to 100 nm range is considered the nanoscale because materials within this size range often exhibit unique physical, chemical, and biological properties that differ significantly from their bulk counterparts. This is due to quantum mechanical effects and a large surface area-to-volume ratio.

Different units of measurement relate to nanometers as follows: 1 Ångstrom (Å) = 0.1 nm, 1 micrometer (µm) = 1000 nm, 1 millimeter (mm) = 1,000,000 nm. Option A (1 Å – 10 nm) is a narrower range within the nanoscale. Options C and D represent the microscale and millimeter scale, respectively, which are much larger than the nanoscale.

37. The resistivity $\rho$ of a material may be expressed in units of

The resistivity $\rho$ of a material may be expressed in units of

ohm

ohm/cm

ohm-cm

ohm-cm$^2$

This question was previously asked in

UPSC CDS-1 – 2020

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Resistivity ($\rho$) is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. Resistance ($R$) of a conductor is related to its resistivity, length ($L$), and cross-sectional area ($A$) by the formula $R = \rho \frac{L}{A}$. Rearranging this formula to solve for $\rho$, we get $\rho = R \frac{A}{L}$.

The unit of resistance ($R$) is Ohm ($\Omega$). The unit of area ($A$) is typically square meters (m²) or square centimeters (cm²). The unit of length ($L$) is typically meters (m) or centimeters (cm). Substituting these units into the formula for $\rho$: $\text{Units of } \rho = \Omega \times \frac{\text{cm}^2}{\text{cm}} = \Omega \cdot \text{cm}$. Alternatively, using meters: $\text{Units of } \rho = \Omega \times \frac{\text{m}^2}{\text{m}} = \Omega \cdot \text{m}$. Therefore, the resistivity is commonly expressed in ohm-centimeters ($\Omega \cdot \text{cm}$) or ohm-meters ($\Omega \cdot \text{m}$).

While both ohm-meter ($\Omega \cdot \text{m}$) and ohm-centimeter ($\Omega \cdot \text{cm}$) are valid units for resistivity, ohm-centimeter is also widely used, particularly in semiconductor physics and some older standards. Option C correctly identifies ohm-cm as a unit for resistivity.

38. The unit of the force constant $k$ of a spring is

The unit of the force constant $k$ of a spring is

N-m

N/m

N-m$^2$

N/m$^2$

This question was previously asked in

UPSC CDS-1 – 2020

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According to Hooke’s Law, the force (F) required to extend or compress a spring by a distance (x) is proportional to that distance, i.e., $F = kx$, where k is the force constant (also known as the spring constant). To find the unit of k, we can rearrange the formula: $k = F/x$. The standard unit of force (F) is Newtons (N), and the standard unit of displacement (x) is meters (m). Therefore, the unit of the force constant k is Newtons per meter (N/m).

– Hooke’s Law: $F = kx$.
– F is force (unit: N).
– x is displacement (unit: m).
– k is the force constant.

The force constant k is a measure of the stiffness of the spring; a higher value of k means the spring is stiffer and requires more force to extend or compress it by a given distance.

39. Which one of the following is the value of one nanometer?

Which one of the following is the value of one nanometer?

10-7 cm

10-6 cm

10-4 cm

10-3 cm

This question was previously asked in

UPSC CDS-1 – 2018

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One nanometer (nm) is a unit of length equal to 10⁻⁹ meters (m). To convert meters to centimeters (cm), we use the conversion factor 1 m = 100 cm = 10² cm.
So, 1 nm = 10⁻⁹ m = 10⁻⁹ × (10² cm) = 10⁻⁹⁺² cm = 10⁻⁷ cm.

– The prefix ‘nano’ (n) represents a factor of 10⁻⁹.
– The base unit of length in SI is the meter (m).
– 1 meter = 100 centimeters = 10² cm.
– To convert from meters to centimeters, multiply by 10².

Nanometers are commonly used to measure wavelengths of visible light, distances in atomic and molecular structures, and in nanotechnology. Other related units include micrometers (µm, 10⁻⁶ m) and picometers (pm, 10⁻¹² m).

40. The SI unit of mechanical power is :

The SI unit of mechanical power is :

Joule

Watt

Newton-second

Joule-second

This question was previously asked in

UPSC CDS-1 – 2016

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The SI unit of mechanical power is Watt.

Power is defined as the rate at which work is done or energy is transferred. In the International System of Units (SI), the unit of work or energy is the Joule (J), and the unit of time is the second (s). Therefore, the unit of power is Joule per second (J/s), which is defined as the Watt (W).

Joule is the SI unit of energy or work. Newton is the SI unit of force. Newton-second is the unit of impulse (force multiplied by time). Joule-second is not a standard unit for power or related quantities; it would represent energy multiplied by time.