Test: Units and Measurements - Grade 12 MCQ

Concept

• Frequency (f): The number of oscillations or the number of waves passes a given point in one sec.
  • Its SI unit is Hertz.
  • Mathematically it can be written as

f = 1/T
Where T =Time and f = frequency

• Dimensional formula of time = [T]
• Dimensional formula of frequency (f) = [M⁰L⁰T^-1]

Explanation

• The frequency of oscillations generated by the LC circuit entirely depends on the values of the capacitor and inductor and their resonance condition.
• It can be expressed as:

Where L = Inductor and C = capacitor

• From the above, it is clear that the dimension of C/L not the dimensions of frequency. 

Concept:
When a force is applied on an object which causes displacement along the direction of force then the work is said to be done by that force.
The work done by a force is defined as: The product of the component of the applied force on the block in the direction of the displacement and the magnitude of this displacement is called work done.
i.e., 
Here both force and displacement will be along the same direction, since force is cause this displacement thus Work done is a scalar quantity.
And SI unit of Work is Joule whereas CGS unit is erg

• Whereas, 1 joule = 10⁷ erg

Explanation:
From the above explanation we can see that both Joule and Erg are units of Works.
Thus, the conversion from joule to erg can be given as
1 joule = 10⁷ erg
Which means option 2 is correct among all

Concept

• Significant Figures: Significant figures in the measured value of a physical quantity tell the number of digits in which we have confidence.
• The larger the number of significant figures obtained in a measurement, the greater is the accuracy of the measurement and vice-versa.
• Significant figures do not change if we measure a physical quantity in different units.
• Significant figures retained after the mathematical operation (like addition, subtraction, multiplication, and division) should be equal to the minimum significant figures involved in any physical quantity in the given operation.
• Significant figures are the number of digits up to which we are sure about their accuracy.

Explanation:

• Trailing zeros or the zeros placed to the right of the number is significant.
• Therefore, 433.00 has five significant figures. So option 4 is correct.

Concept

• A physical quantity is a property of a material. It can be expressed in number by measurement.
• A physical quantity is expressed by a numerical value and a unit. For example, the physical quantity length can be expressed as 4 meters, where 4 is the numerical value and meter is the unit.
• The SI units are the standard units of measurement defined by the International System of Units (SI).

Explanation
Following are the SI units of the physical quantity:

The kilogram represents the unit of a physical quantity and not the physical quantity. Therefore option 4 is correct.

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.

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

Concept:

• There are 7 base Units, which are - 
• Length (Metre), Time (Second), Amount of Substance (Mole), Electric Current (Ampere), Temperature (Kelvin), Luminous Intensity (Candela) and Mass (Kilogram).
• All the other Units other than the base units are called "Derived SI Units".

Explanation:

• As explained earlier Magnetic field is derived quantity
• Whereas Tesla is the unit of Magnetic field strength.

Note:

• Some Popular SI Units are

Concept

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities. 
• The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
• And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

Explanation

Strain:

• The ratio of change in configuration to the original configuration is called strain.

• As the strain is the ratio of two like quantities, it has no units and no dimensions.
•  and has no dimension.
• Its dimension can be expressed as M⁰L⁰T⁰.

​The correct answer is M⁰L⁰T⁰​.

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

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

• The SI unit is an international system of units used in technical and scientific research to minimize confusion with measuring units.
• There are two types of quantities
  • Fundamental quantities or base quantities

• Derived quantities are those quantities derived from the base quantities 
• Acceleration is the rate at which velocity changes with respect to time
• Acceleration is derived quantities from length and time
• S.I. Unit of acceleration is ms^-2 

Concept:

The dimensional formula of energy is given by,
M¹ L² T^-2 
Where,

• M = Mass
• L = Length
• T = Time

Energy = m × c² 
Where m = mass
c = velocity
velocity (c) = Distance × [Time]-1 = M⁰ L¹ T^-1
∴ The dimensional formula of velocity = M⁰ L¹ T^-1
Energy = m × c²
Or, E = [M] × [L¹ T^-1]² = M¹ L² T^-2.
Therefore, energy is dimensionally represented as M¹ L² T^-2.