Free Errors and Significant Figures MCQs with Answers

11. The given diagram shows two different scales on a Vernier callipers. The reading on the Vernier scale is

• A. 0.5
• B. 5
• C. 6.5
• D. 7

Explanation: Read the main scale reading (MSR):Observe the mark on the main scale that is just before the zero mark of the Vernier scale. In the given diagram, the zero mark of the Vernier scale is past the 6.5 cm mark on the main scale but before the 6.6 cm mark. Therefore, the MSR is 6.5 cm.2. Read the Vernier scale coincidence (VSC):Find the mark on the Vernier scale that perfectly aligns with any mark on the main scale. In the diagram, the 5th division of the Vernier scale aligns with a mark on the main scale. So, the VSC is 5.3. Calculate the least count (LC):The least count of a Vernier caliper is typically 0.01 cm (assuming 10 divisions on the Vernier scale match 9 divisions on the main scale, and the smallest division on the main scale is 0.1 cm).4. Calculate the total reading:The total reading is given by the formula: Total Reading = MSR + (VSC × LC).Total Reading = 6.5 cm + (5 × 0.01 cm) = 6.5 cm + 0.05 cm = 6.55 cm.

12. Which of the given sources of errors will NOT affect your readings while handling the Gravesand's apparatus?

• A. Friction in the pulleys
• B. Use of rusty holding pins
• C. Use of inaccurate weights
• D. Placement of the drawing board

Explanation: Friction in the pulleys is the correct answer because it directly impacts the smooth movement of the apparatus, affecting the accuracy of the readings. The other options, such as rusty holding pins, inaccurate weights, and the placement of the drawing board, can all introduce errors but may not necessarily be exclusive to Gravesand's apparatus or have the same direct impact on readings.

13. A student performs an experiment in his college laboratory to determine the specific heat of water by electrical method. At the end of experiment, the graph that he drew betweentemperature (T) and time (t) was incorrect.Which of the following can be a source of error that caused inaccurate reading during his observation?

• A. Loss of heat due to radiation
• B. Large increase in temperature of water
• C. Greater least count of the thermometer
• D. Non-steady voltage of the power supply

Explanation: The correct answer is option C: Greater least count of the thermometer. In experiments involving precise temperature measurements, having a greater least count on the thermometer can introduce errors in the readings, resulting in an incorrect graph. The other options, such as loss of heat due to radiation, large increase in temperature of water, and non-steady voltage of the power supply, are less likely to directly cause inaccuracies in the graph between temperature and time in this specific experimental setup.

14. A student makes measurements from which she calculated the speed of sound as 321 ms-1 . She estimates that the result is accurate to +3% or -3% . Which of the following give results expressed to the appropriate number of significant figures?

• A. 327 ms-1
• B. 328 ms-1
• C. 330 ms-1
• D. 300 ms-1

Explanation: a) 327 m/s:This option provides a result with three significant figures. However, the given measurement is accurate to +3% or -3%, which means the uncertainty in the measurement is ±3%. Therefore, the appropriate number of significant figures should consider the uncertainty, and in this case, it should be expressed as 321 ± 3 m/s. Rounded to three significant figures with the appropriate uncertainty, it would be written as 321 ± 3 m/s.

15. The density of a steel ball was determined by measuring its mass and diameter. The mass was measured within 1% and the diameter with 3%. The error in the calculated density of the steel ball is at most:

• A. 10%
• B. 4%
• C. 3%
• D. 2%

Explanation: b) 4%:This option suggests that the maximum error in the calculated density of the steel ball is 4%. While this seems reasonable, let's examine the errors in measuring the mass and diameter to confirm if this is accurate.