unit 1

Physics 1 Marks

1. Define physical quantity.

A physical quantity is a property of a material or a system that can be measured, such as length, mass, time, or temperature.

2. Define fundamental physical quantity.

A fundamental physical quantity is a physical quantity that cannot be expressed in terms of other physical quantities. Examples include length (meter), mass (kilogram), and time (second).

3. Define derived physical quantity.

A derived physical quantity is a physical quantity that is expressed in terms of one or more fundamental physical quantities. Examples include area (length2), velocity (length/time), and density (mass/volume).

4. Define unit.

A unit is a standard measure used to express a physical quantity. For example, the meter is the unit of length, and the kilogram is the unit of mass.

5. Define dimensions.

The dimensions of a physical quantity are the powers to which the fundamental quantities (like mass, length, and time) must be raised to represent that quantity. For example, the dimensions of velocity are [M0L1T−1].

6. Define dimensional formula.

A dimensional formula is an expression that shows how and which of the fundamental quantities are included in a derived quantity. For example, the dimensional formula for force is [M1L1T−2].

7. State the principal of homogeneity of dimensions.

The principal of homogeneity of dimensions states that an equation is dimensionally correct if the dimensions of the terms on both sides of the equation are the same. This means you can only add or subtract physical quantities that have the same dimensions.

8. Define absolute error.

The absolute error in a measurement is the magnitude of the difference between the true value and the measured value of a quantity.

9. Define percentage error.

The percentage error is the relative error expressed as a percentage. It is calculated as:

Percentage Error=(Absolute Error/True Value)×100%

Physics 3 Marks

1. Define fundamental and derived physical quantities and give one example for each.

Fundamental physical quantities are independent of each other and cannot be expressed in terms of other quantities.

  • Example: Mass (unit: kilogram).

    Derived physical quantities are those whose defining operations are based on other fundamental quantities.

  • Example: Velocity (unit: m/s).

2. Write any three advantages of SI units.

  1. Universality: The SI system is a globally accepted and used system of units, making it easy to communicate scientific and technical data worldwide.

  2. Coherence: It is a coherent system where all derived units are obtained from fundamental units without introducing numerical factors. For instance, the unit of force (newton) is simply .

  3. Rationality: It is a rational system where only one unit is used for a particular physical quantity, avoiding confusion (e.g., all forms of energy are measured in joules).

3. Explain principle of homogeneity of dimensions.

The principle of homogeneity of dimensions is a fundamental concept in dimensional analysis. It states that an equation is dimensionally correct if the dimensions of all the terms on both sides of the equation are identical. This principle implies that you can only add, subtract, or equate physical quantities that have the same dimensions. For example, in the equation s=ut+21​at2, each term (s, ut, and 21​at2) must have the dimensions of length [L].

4. Write three applications of dimensional analysis.

  1. To check the correctness of a physical equation: By ensuring that the dimensions of all terms on both sides of an equation are the same, you can verify if the equation is dimensionally correct.

  2. To derive the relationship between physical quantities: It can be used to determine how different physical quantities are related to each other, although the constant of proportionality cannot be determined.

  3. To convert a physical quantity from one system of units to another: Using dimensional analysis, you can find the conversion factor to change the units of a quantity (e.g., converting a force from newtons to dynes).

5. State the principle of homogeneity of dimensions and write any two applications of dimensional analysis.

Principle of Homogeneity of Dimensions: As stated above, this principle asserts that in any correct physical equation, the dimensions of each term on both sides of the equation must be the same.

Two applications of dimensional analysis:

  1. Checking the correctness of an equation: Ensures dimensional consistency.

  2. Deriving relationships between physical quantities: Helps to find how different variables in a physical phenomenon are related.

6. Define dimensions and write any two applications of dimensional analysis.

Dimensions: The powers to which the fundamental quantities (mass, length, time, etc.) are raised to express a derived physical quantity.

Two applications of dimensional analysis:

  1. Checking dimensional consistency of equations.

  2. Converting units from one system to another.

7. List any three limitations of dimensional analysis.

  1. The value of dimensionless constants cannot be determined: Dimensional analysis cannot give you the numerical value of constants like ฯ€ or k in an equation.

  2. It cannot be used for equations involving trigonometric or logarithmic functions: Equations with these functions cannot be analyzed using this method because these functions are dimensionless.

  3. It cannot determine if a quantity is a scalar or a vector: It only deals with dimensions, not the directional nature of quantities.

8. Define absolute error and percentage error.

Absolute error: The magnitude of the difference between the true value and the measured value of a quantity.

Percentage error: The relative error multiplied by 100. It is a more meaningful way to express error, as it relates the error to the magnitude of the measured value.

Physics 5 Marks

1. Write any five advantages of SI units.

  1. Coherent System: All derived units are obtained from fundamental units without introducing any numerical factors.

  2. Rational System: One unit is used for a single physical quantity, which avoids confusion. For example, the joule is used for all forms of energy.

  3. Metric System: Multiples and sub-multiples of units are expressed as powers of 10, which simplifies calculations.

  4. Universal Acceptance: It's used globally in science, technology, and trade, making it a standard language for measurement.

  5. Easy to Use: It's based on a decimal system, making conversions straightforward and logical.

2. Write any five limitations of dimensional analysis.

  1. Value of dimensionless constants: It cannot determine the value of a dimensionless constant in an equation.

  2. Trigonometric and exponential functions: The method fails for equations containing trigonometric functions (like sinฮธ,cosฮธ) or exponential functions, as they are dimensionless.

  3. Addition and subtraction: It cannot determine whether a quantity should be added or subtracted in an equation.

  4. Nature of quantities: It doesn't provide information about whether a physical quantity is a scalar or a vector.

  5. Equations with multiple terms: It can't be used to derive an equation that has more than one term on one side (e.g., ).

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