Errors in Measurement โ Types and Rules - UNSOLVED PRACTICE SET
Chapter: Physical World and Measurement | Topic: Errors in Measurement Types and Rules
ERRORS IN MEASUREMENT โ TYPES AND RULES - UNSOLVED PRACTICE SET
Topic: Errors in Measurement Types and Rules
Multiple Choice Questions
Q1. The difference between the measured value and the true value of a quantity is called:
- Precision
- Accuracy
- Error
- Uncertainty
Q2. Systematic errors are those that:
- Occur randomly and can be positive or negative
- Occur due to known causes and follow a definite pattern
- Can be completely eliminated by taking more readings
- Are caused only by the observer's carelessness
Q3. Random errors can be reduced by:
- Calibrating the instrument properly
- Taking a large number of observations and finding the mean
- Eliminating the source of error
- Using a more precise instrument only
Q4. The least count of a vernier caliper is 0.01 cm. The maximum possible error in a measurement made with this instrument is:
- 0.001 cm
- 0.01 cm
- 0.1 cm
- 1.0 cm
Q5. If a quantity is measured as (50 ยฑ 2) cm, the percentage error is:
- 1%
- 2%
- 3%
- 25%
Q6. The absolute error in the sum of two quantities is
- The sum of their absolute errors
- The difference of their absolute errors
- The product of their absolute errors
- The ratio of their absolute errors
Short Answer Questions
Q7. Distinguish between systematic errors and random errors. Give one example of each.
Q8. Define:
(a) Absolute error
(b) Relative error
(c) Percentage error
Q9. A student measures the length of a table five times and gets the readings: 150.2 cm, 150.0 cm, 150.3 cm, 150.1 cm, and 150.4 cm. Calculate the mean value and the absolute error in each reading.
Q10. In your school physics lab, you are given a metre scale, a vernier caliper, and a screw gauge to measure the diameter of a pencil. Which instrument would give the most precise measurement, and why? What type of error would you encounter if the screw gauge had a zero error
Q11. Explain the difference between accuracy and precision with a suitable example. Can a measurement be precise but not accurate?
Q12. What are gross errors? How can they be minimised in a laboratory experiment?
Long Answer Questions
Q13. Discuss the various types of errors in measurement:
(i) Systematic errors (with subtypes: instrumental, environmental, observational)
(ii) Random errors
(iii) Gross errors
For each type, explain the cause, effect, and method of minimisation.
Q14. Explain the rules for combining errors:
(i) Error in the sum or difference of two quantities
(ii) Error in the product or quotient of two quantities
(iii) Error in a quantity raised to a power
Derive the general formula for each case and illustrate with examples.
Q15. A student performs an experiment to determine the density of a metal block. The measurements are:
Mass: (250.0 ยฑ 0.5) g
Length: (5.0 ยฑ 0.1) cm
Breadth: (4.0 ยฑ 0.1) cm
Height: (2.0 ยฑ 0.1) cm
Analyse how errors in each measurement propagate to the final calculated density. Which measurement contributes most to the uncertainty in density? Suggest how the student could improve the experiment.
Application-Based Problems
Q16. In a school experiment, the time period of a simple pendulum is measured 10 times, yielding the following readings (in seconds):
2.02, 2.05, 2.00, 2.03, 2.04, 2.01, 2.06, 2.02, 2.03, 2.05
(a) Calculate the mean time period.
(b) Calculate the absolute error in each observation.
(c) Calculate the mean absolute error.
(d) Express the time period with the correct error limit.
(e) Calculate the relative error and percentage error.
Q17. The resistance R of a wire is calculated using the formula R = V/I, where V = (10.0 ยฑ 0.1) volts and I = (2.0 ยฑ 0.1) amperes.
(a) Calculate the value of R.
(b) Calculate the maximum possible error in R using the rules of error propagation.
(c) Express R with its uncertainty.
(d) Calculate the percentage error in R.
(e) If the student wants to reduce the percentage error to less than 2%, suggest which measurement should be improved and how.
Q18. A student is asked to determine the value of acceleration due to gravity g using a simple pendulum. The formula is g = 4ฯยฒL/Tยฒ. The student measures:
Length L = (100.0 ยฑ 0.1) cm
Time for 20 oscillations = (40.0 ยฑ 0.2) s
(a) Calculate the time period T.
(b) Calculate the value of g.
(c) Calculate the error in g using error propagation rules.
(d) Express g with its uncertainty.
(e) The accepted value of g in Delhi is approximately 9.79 m/sยฒ. Is the student's result consistent with this value? If not, what type of error might be present?