Error Analysis - NEET Physics Questions
Question 21: easy

Taking into account of the significant figures, what is the value of \(9.99 \text{m} – 0.0099 \text{m}\)?

[NEET 2020]

1. \(9.98 m\)
2. \(9.980 \text{m}\)
3. \(9.9 \text{m}\)
4. \(9.9801 \text{m}\)
View Answer

The numbers are \(9.99 \text{m}\) (2 decimal places) and \(0.0099 \text{m}\) (4 decimal places). For subtraction, the result should have the same number of decimal places as the number with the fewest decimal places (2 in this case). \(9.9900 - 0.0099 = 9.9801\). Rounding \(9.9801\) to 2 decimal places gives \(9.98 \text{m}\).

Question 22: moderate

The diameter of a spherical bob, when measured with vernier callipers yielded the following values: 3.33 cm, 3.32 cm, 3.34 cm, 3.33 cm and 3.32 cm. The mean diameter to appropriate significant figures is:

1. 3.33 cm
2. 3.32 cm
3. 3.328 cm
4. 3.3 cm
View Answer

The mean of the values is \[\frac{3.33 + 3.32 + 3.34 + 3.33 + 3.32}{5} = 3.328 \text{cm}\]. Since the measurements are up to two decimal places, the rounded final result should also have two decimal places: 3.33 cm.

Question 23: easy

Following observations were taken with a vernier calliper while measuring the length of a cylinder: \(3.29 \text{cm}\), \(3.28 \text{cm}\), \(3.29 \text{cm}\), \(3.31 \text{cm}\), \(3.28 \text{cm}\). The most accurate length of the cylinder will be

1. \(3.28 \text{cm}\)
2. \(3.29 \text{cm}\)
3. \(3.32 \text{cm}\)
4. \(3.21 \text{cm}\)
View Answer

The most accurate value is the mean value of the observations. Mean length = \[\frac{3.29 + 3.28 + 3.29 + 3.31 + 3.28}{5} = \frac{16.45}{5} = 3.29 \text{cm}\].

Question 24: moderate

Consider the given statements:


Statement A: Measured value by any measuring instrument has some error.


Statement B: A measurement can have more accuracy and less precision and vice-versa.


Statement C: The magnitude of the difference between the true value of the quantity and the individual measured value is called relative error of measurement.


Choose the correct option.

1. Only statement A is true
2. Only statement B is true
3. Both statements A and C are true
4. Both statements A and B are true
View Answer

Statements A and B are correct properties of measurements. Statement C is incorrect because the described quantity is the absolute error, not the relative error.

Question 25: easy

In an experiment, the percentage error occurring in the measurements of physical quantities \( A \), \( B \) and \( C \) are 1%, 2% and 3% respectively. If a physical quantity \( X \) is such that \( X = \frac{AB^2}{C^3} \), then the percentage error in the calculation of \( X \) can be

1. 1%
2. 2%
3. 3%
4. 4%
View Answer

By taking systematic errors into account, the relative error can be written with signs: \( \frac{\Delta X}{X} = \pm \frac{\Delta A}{A} \pm 2\frac{\Delta B}{B} \pm 3\frac{\Delta C}{C} \). The minimum absolute error is \( |1 + 4 - 9|\% = 4\% \), so 4% is a possible value.

Question 26: easy

Sum of the numbers \(436.32\text{ g}\), \(227.2\text{ g}\) and \(0.301\text{ g}\) is

1. 663.821 g
2. 663.8 g
3. 6663.82 g
4. 664 g
View Answer

In addition, the final result must be rounded off to the least number of decimal places of the terms. Here, \(227.2\text{ g}\) has one decimal place, so the sum \(663.821\text{ g}\) is rounded to \(663.8\text{ g}\).