The international system of units MCQ Quiz - Objective Question with Answer for The international system of units - Download Free PDF

Calculation: 

The unit of relative permittivity

Relative permittivity, also known as the dielectric constant, is a dimensionless quantity. It is the ratio of the permittivity of a substance to the permittivity of free space (vacuum).

Since it is a ratio of two quantities with the same unit, the unit of relative permittivity is unitless.

∴ The correct answer is option 3

Concept Used:

The given equation is:

P = ρⁿ v²

We need to find the value of n, and to do this, we will perform dimensional analysis. The dimensions of each quantity involved are as follows:

The dimensions of pressure P are: [P] = M L^-1 T^-2

The dimensions of density ρ are: [ρ] = M L^-3

The dimensions of velocity v are: [v] = L T^-1

Substitute these dimensions into the given equation:

[P] = [ρⁿ] [v²]

Calculation:

Let’s plug in the dimensions:

[M L^-1 T^-2] = [ (M L^-3)ⁿ ] [ (L T^-1)² ]

Simplify the dimensions on the right-hand side:

[M L^-1 T^-2] = [Mⁿ L^-3n] [L² T^-2]

Combine the terms on the right-hand side:

[M L^-1 T^-2] = [Mⁿ L^-3n+2 T^-2]

Now, equate the exponents of corresponding dimensions from both sides:

For mass (M): 1 = n

For length (L): -1 = -3n + 2

For time (T): -2 = -2 (This is already satisfied)

From the mass dimension equation, we get:

n = 1

To verify, substitute n = 1 in the length dimension equation:

-1 = -3(1) + 2

-1 = -3 + 2

-1 = -1

This is correct, so the value of n is confirmed as:

n = 1

Therefore, the correct option is:

Option 2: n = 1

The correct answer is a - ii, b - iii, c = iv, d - i.

The correct match:

The correct answer is m/s

Key Points

• Velocity: The rate of change of displacement of a body is called the velocity of that body.

​\(\Rightarrow Velocity=\frac{Displacment (x)}{Time (t)}\)

• Velocity is a vector quantity that has both magnitudes as well as direction.

EXPLANATION:

• The unit of velocity is m/s and the dimension of velocity is [M0LT-1].

The correct answer is option 1) i.e. joule (J)

CONCEPT:

• Work function: It is the minimum amount of energy required to cause photo-emission of electrons from a metal surface when light is incident on it.
  • The work function is also known as the threshold energy.
  • The energy of the incident light is equal to the sum of the work function and the photoelectron kinetic energy.

  • Therefore, the total energy of photon = work function + maximum kinetic energy of the electron.

The energy of a photon is given by the equation:

 \(E =hν\)

Where ν is the frequency of incident light and h is the Planck's constant.​

EXPLANATION:

• The work function is a measure of energy. All forms of energy have the same SI unit i.e. joule (J).

CONCEPT:

• The standard units of measurement defined by the ISU for the seven base quantities are SI base units.
• All other SI units are derived from them.
• 7 Basic SI units with their quantities: 

EXPLANATION:

• From the above table, it is clear that Candela is a unit of luminous intensity. Therefore option 4 is correct. 

Important Points

• Supplementary units: The units that are used along with base units to form derived units in the International System are called supplementary units.

Concept:

Capacitance

• Capacitance is a property of the electric conductor measured by the amount of separated electric charge that can be stored on it per unit change in electrical potential.
• In capacitor, amount of charge, Q = CV, where, C = Capacitance, V = electrical potential
• A capacitance in an electric circuit is introduced by a device called a capacitor.
• The SI unit of the capacitance is Farad and is denoted by the F.

Explanation:

The SI unit of capacitance is Farad denoted by F.

Additional Information

• Resistance
  • ​​Resistance in an electric circuit is introduced by a device called a resistor.
  • Formula, V = IR, where I = electric current flowing in the circuit, V =  supplied voltage, R = Resistance
  • The SI unit of resistance is Ohm denoted by Ω.
• Conductance
  • ​The reciprocal of the resistance In a conductor is called conductance.
  • Relation, \(Conductance=\frac{1}{Resistance}\)
  • The SI unit of conductance is Ohm^-1.
• Inductance
  • ​The inductance in an electric circuit is introduced by a device called an inductor. 
  • The SI unit of the inductance is Henery denoted by H.

The correct answer is option 2) i.e. 105 N/m2

CONCEPT:

• Système International (SI) unit is the metric system used for standard measurements of quantities.
  • It is also known as the MKS system.
  • This system considers metre (m) as the unit of length, kilogram (kg) as the unit of mass, and second (s) as the unit of time.
• CGS system considers centimetres (cm) as the unit of length, gram (g) as the unit of mass, and second (s) as the unit of time.

EXPLANATION:

• Dyne is the cgs unit for force. The SI unit of force is N.
• cm² is the cgs unit for the area. The SI unit for the area in m².
• Hence, the SI unit for atmospheric pressure is N/m².
• 1 dyne is equal to the force that would give a free mass of 1 g acceleration of 1 cm/s².

⇒ 1 dyne = 1 g × 1 cm/s²

⇒ 1 dyne = 10^-3 kg × 10^-2 m/s²  (∵ 1 m = 100 cm and 1 kg = 1000 g)

⇒ 1 dyne = 10^-5 N

⇒ 106 dyne/cm2 = \(\frac{10^{6} \times 10^{-5}N}{(10^{-2})^2m^2} = 10^5 \:N/m^2\)

Explanation:

• Force (F): The interaction which after applying on a body changes or try to change the state of rest or state of motion of a body is called force.
  • The SI unit of force is Newton (N)

Force (F) = Mass (m) × acceleration (a)

• Pressure (P): The force per unit area is called pressure.
• The SI unit of pressure is the pascal (Pa) 
• It can also be written as Newton /meter2 that is unit of force divided by unit of area. 
• The other units of pressure are Bar and torr. 

Additional Information

•  The SI units are internationally accepted units. 
• SI unit of work and energy is Joule. 
• SI unit of power is Watt. 

The correct answer is option 2) i.e. kg m3 s-3 A^-1

CONCEPT:

• Electric flux: It is the number of electric field lines passing through a given surface area. The electric flux associated with a surface kept in a uniform electric field is given by

ϕ = E.A = EAcosθ 

Where E is the uniform electric field, A is the area of the surface and θ is the angle between E and area vector of A.

• The SI base units are the standard units of measurement.
  • ​The seven base units used in SI system are: meter (m), kilogram (kg), second (s), kelvin (K), ampere (A), mole (mol), and candela (cd).

EXPLANATION:

• The SI unit of the electric field is N C^-1 and the SI unit for area is m². Hence the SI unit for electric flux is N m² C^-1.
• N is the SI unit of force, which is obtained from the product of mass and acceleration. F = ma.
  • Therefore, the base units for N is kg m s^-2.
• C is the SI unit for electric charge. We know, charge = current × time. The units for current is A and time is s.
  • Therefore, the base units of C is A s

​On substituting these to N m² C^-1,

⇒ (kg m s^-2) (m²) (A s)^-1 = kg m³ s-3 A^-1 

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.
  • The SI unit of force is Newton.
• Magnetic field: The region around a magnet or a current-carrying wire in which the magnetic force on the other magnet can be experienced is called a magnetic field.
  • The SI unit of the magnetic field is the tesla (T).
• Radioactivity: Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive.
  • The original unit for measuring the amount of radioactivity is the curie (Ci) – first defined to correspond to one gram of radium-226.
  • 1 curie = 3.7x1010 radioactive decays per second.
  • In the International System of Units (SI) the curie has been replaced by the becquerel (Bq).
  • 1 becquerel = 1 radioactive decay per second = 2.703x10-11 Ci.​
• Capacitance: The capacity of a capacitor to store electric charge is called capacitance.
  • The unit of capacitance is the farad, (symbol F ).

EXPLANATION:

From the above discussion, we can say that

• Options 1, 2, and 3 are correctly matched with their respective SI units.
• But the SI unit of capacitance is Farad, so option 4 is wrong.

CONCEPT:

• Induction: It is the magnetic field that is proportional to the rate of change of the magnetic field.
  • This definition of induction holds for a conductor. Induction is also known as inductance.
  • L is used to represent the inductance and Henry is the SI unit of inductance.
  • 1 Henry is defined as the amount of inductance required to produce an emf of 1 volt in a conductor when the current change in the conductor is at the rate of 1 Ampere per second.
  • Following are the factors that affect the inductance:
  1. The number of turns of the wire used in the inductor.
  2. The material used in the core.
  3. The shape of the core.
  • Electromagnetic Induction: The law was given by Faraday which states that by varying the magnetic flux electromotive force is induced in the circuit.
  • Inductance: It can be defined as the electromotive force generated to oppose the change in current at a particular time duration.

 According to Faraday’s Law:

\(E.M.F = -L\frac{\Delta I}{\Delta t}\)

\(Unit = \frac{Volts \times second}{Ampere} = Henry\)

EXPLANATION:

• From the above discussion, it's clear that the unit of inductance is Henry.

The correct option is 2.

Additional Information

• Unit of capacitance: Farad
• Unit of magnetic intensity: W/m²
• Unit of Frequency: Hertz

CONCEPT:

• Unit: The unit is the chosen standard used for measuring a physical quantity. It is also used for taking any comparisons in measurements.
  • The conversions of units allow for measurements of a property that has already recorded through different units.
  • For example, centimeters to inches.
• Types of Unit: 
  • There are two main types of Units are present. which are as follows-
• Fundamental units: The Fundamental Quantity is an independent Physical Quantity that cannot be expressed in terms of other Physical Quantities.
  • They are conventionally chosen.
  • It is used as a base to get other derived quantities by combining them.

There are 7 fundamental quantities.

• Derived Unit: The combination of two base units that means fundamental units that express a physical quantity.
  • It is presented by SI units.  For example, the velocity is the distance(m) traveled per unit time(s)
  • so we can say the derived unit of velocity is 'm/s.

EXPLANATION:

• There are two types of units. So option 1 is correct. 

CONCEPT:

• Newton's law of gravitation: The gravitational force between two objects is directly proportional to the product of masses of the objects and inversely proportional to the distance between two mass.

i.e., \(F = \frac{{GMm}}{{{R^2}}}\)

whereas according to classical mechanics force acting on the particle is given as

Force (F) = mass (m) × acceleration (a)

Where, F = gravitational force, M = mass of a heavier object, m = mass of a lighter object, R = distance between two masses

EXPLANATION:

Now using the above equation, we can say that \(G = \frac{{F{R^2}}}{{Mm}}\)

The SI unit of force is the Newton (N).

The SI unit of distance (R) is meter (m) and the SI unit of mass is kg.

The SI unit of G = N m²/kg²

So option 3 is correct.