Applied Physics Chapter 1

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Questions and Answers

What is the main purpose of a vernier calliper?

To measure the distance between two symmetrical points (correct)

To assess the weight of an object

To measure temperature in environments

To measure angles with high precision

Which part of the vernier calliper is utilized to measure internal lengths?

Outside Jaws

Inside Jaws (correct)

Depth Probe

Main Scale (cm)

What geometry concept is illustrated by translating two vectors to form a parallelogram?

Vector summation and difference (correct)

Vector rotation

Vector projection

Vector normalization

How is the vector difference represented in the parallelogram constructed from two vectors?

As a diagonal opposite the resultant vector Signup and view all the answers

Which measurement tool is typically used in combination with the tips of a vernier calliper?

Ruler Signup and view all the answers

Which part of the vernier calliper is specifically designed to measure depths?

Depth Probe Signup and view all the answers

In which fields is a vernier calliper commonly utilized?

Metal working and woodworking Signup and view all the answers

When constructing a parallelogram using two vectors, what does the diagonal from the origin to the opposite corner represent?

The resultant vector of the two original vectors Signup and view all the answers

Which of the following is NOT a source of systematic errors?

Random fluctuations in environmental conditions Signup and view all the answers

What type of error is introduced when there is a zero error in an instrument?

Instrumental error Signup and view all the answers

Which of the following factors can systematically impact measurement results?

Improperly calibrated thermometers Signup and view all the answers

In what situation would a thermometer reading lower than the actual body temperature be expected?

Thermometer placed under the armpit Signup and view all the answers

Which of the following best describes random errors?

Errors arising from unpredictable fluctuations Signup and view all the answers

What type of error might occur due to an individual's consistent bias while reading measurements?

Systematic error Signup and view all the answers

What is the consequence of a worn-off measuring scale edge?

Systematic errors in measurements Signup and view all the answers

What could cause a thermometer to read inaccurately at the boiling point of water?

Incorrect temperature scale readings Signup and view all the answers

What are fundamental or base units?

Units used for expressing physical quantities without combination Signup and view all the answers

Which of the following is NOT a base unit in the SI system?

Pound Signup and view all the answers

How many base units are defined in the SI system?

7 Signup and view all the answers

Which of the following systems was NOT historically in widespread use for measurement?

PQS system Signup and view all the answers

What is the primary purpose of the International System of Units (SI)?

To standardize measurements for scientific and industrial purposes Signup and view all the answers

Which base quantity is represented by the unit 'lumen'?

Illuminance Signup and view all the answers

Which of the following is true about derived units?

They are combinations of base units. Signup and view all the answers

What was the main reason for developing the SI system?

To unify different countries' measurement systems Signup and view all the answers

What primarily differentiates vector quantities from scalar quantities?

Vectors have both magnitude and direction. Signup and view all the answers

Which operation cannot be performed with vector quantities?

Dividing one vector by another Signup and view all the answers

What is required to accurately draw vectors in a plane following the geometric approach?

Rulers, a protractor, and geometric tools Signup and view all the answers

The parallelogram rule is used for what purpose in vector analysis?

To find the resultant of two vectors in a plane Signup and view all the answers

What complicates the addition of vectors compared to scalar addition?

The dependence on geometry and trigonometry Signup and view all the answers

Which of the following is NOT considered a vector quantity?

Energy Signup and view all the answers

In a two-dimensional plane, what must be applied to calculate vector magnitudes and directions after determining resultant vectors?

Geometry and algebra together Signup and view all the answers

When combining vectors using the laws of algebra, which statement is accurate?

The parallelogram rule is irrelevant in one-dimensional analysis. Signup and view all the answers

What is the formula used to calculate the mean absolute error (∆amean)?

∆amean = (|∆a1| + |∆a2| + ... + |∆an|) / n Signup and view all the answers

In the context of measurement errors, what does the relative error represent?

The mean absolute error divided by the mean value of the measured quantity. Signup and view all the answers

How is the percentage error (δa) calculated from the relative error?

δa = (relative error) × 100% Signup and view all the answers

Given the periods of 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s, what is the mean period of oscillation (Tmean)?

2.62 s Signup and view all the answers

When measuring the period of a pendulum, which of the following represents the calculated absolute error for the reading of 2.56 s?

-0.06 s Signup and view all the answers

If the mean absolute error (∆amean) is calculated as 0.11 s and the mean value (amean) is 2.62 s, what is the relative error (δa)?

0.04 Signup and view all the answers

What is the percentage error if the relative error is calculated as 0.04?

4% Signup and view all the answers

What is the absolute error for the measurement of 2.80 s when the mean period is 2.62 s?

0.18 s Signup and view all the answers

Study Notes

Units and Measurements

Measurement of physical quantities involves comparison with internationally accepted reference standards called units.
Physical quantities are expressed with numerical values paired with units, allowing for a concise description.
Fundamental units are those that describe base quantities; derived units are combinations of these base units.
A complete system, including both base and derived units, is termed a system of units.

International System of Units (SI)

The SI was established to standardize measurements globally, developed in 1971 by the General Conference on Weights and Measures.
Prior systems included CGS (centimetre, gram, second), FPS (foot, pound, second), and MKS (metre, kilogram, second).
SI units are crucial for scientific, technical, industrial, and commercial applications.

Scalars and Vectors

Scalar quantities have magnitude only, e.g., temperature, mass, and energy, and can be added or subtracted like regular numbers.
Vector quantities have both magnitude and direction, e.g., displacement, velocity, and force—represented mathematically as vectors.
Vectors can be added using geometric methods, such as the parallelogram rule to find their resultant.

Parallelogram Rule of Vector Addition

To add two vectors geometrically, translate one vector to the origin of another, forming a parallelogram.
The diagonal of the parallelogram represents the resultant vector.
The other diagonal indicates the difference between the two vectors.

Vernier Calliper

A device for measuring distances between opposing sides, useful in fields like engineering and woodworking.
Components include:
- Outside Jaws: Measure external lengths
- Inside Jaws: Measure internal lengths
- Depth Probe: Measures depth
- Main Scale: Available in cm and inches
- Vernier Scale: Available in cm and inches

Errors in Measurement

Systematic Errors: Consistently biased towards one direction due to factors like:
- Instrumental Errors: Flaws in design or calibration (e.g., thermometer miscalibration).
- Imperfections in technique: External conditions affecting the measurement.
- Personal Errors: Bias or carelessness by the observer.
Random Errors: Occur unpredictably during measurements and vary in sign and magnitude.
Absolute Error: The measure of inaccuracy without reference to the true value.
Relative Error: Ratio of mean absolute error to the mean value of the measured quantity.

Error Calculation

Percentage Error Calculation:
- Relative Error: ( \text{Relative Error} = \frac{\Delta a_{mean}}{a_{mean}} )
- Percentage Error: ( \delta a = \left(\frac{\Delta a_{mean}}{a_{mean}}\right) \times 100% )
Example of period of oscillation in a pendulum illustrates how to calculate absolute, relative, and percentage errors.

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Description

Explore the fundamental concepts of Units and Measurements in Applied Physics. This quiz covers essential principles related to the measurement of physical quantities, reference standards, and the importance of units in scientific analysis.