## Chapter 2 Measurement Errors And Experiments MCQs

**Question 1. Using a screw gauge, the observation of the diameter of a wire is 1.324, 1.326, 1.334, and 1.336 cm respectively. Find the average diameter, the mean error, the relative error, and the % error.**

**Answer: **\(\overline{\mathrm{D}}=1.330 \mathrm{~cm}, \overline{\Delta \mathrm{D}}=0.005 \mathrm{~cm}\) = 1, Relative error = + 0.004 %, error = 0.4%

**Question 2. Round off the following numbers within three significant figures –**

- 0.03927 kg
- 4.085 x 108 sec
- 5.2354 m
- 4.735 x 10–6 kg

**Answer:**

- 0.0393 kg
- 4.08 x 108 sec
- 5.24 m
- 4.74 x 10–6 kg

**Question 3. If a tuning fork of frequency (f0) 340 Hz and tolerance ± 1% is used in the resonance column method [v = 2f 0 (l2 – l1)], the first and the second resonance are measured at l1 = 24.0 cm and l2 = 74.0 cm. Find max—permissible error in speed of sound. **

**Answer:** 1.4%

## Chapter 2 Measurement Errors And Experiments MCQs Part -2 Only One Option Correct Type

**Question 1. The length of a rectangular plate is measured by a meter scale and is found to be 10.0 cm. Its width is measured by vernier calipers as 1.00 cm. The least count of the meter scale and vernier calipers are 0.1 cm and 0.01 cm respectively (Obviously). Maximum permissible error in area measurement is –**

- + 0.2 cm²
- + 0.1 cm²
- + 0.3 cm²
- Zero

**Answer:** 1. + 0.2 cm²

**Question 2. In the previous question, the minimum possible error in area measurement can be** –

- + 0.02 cm²
- + 0.01 cm²
- + 0.03 cm²
- Zero

**Answer:** 4. Zero

**Question 3. For a cubical block, the error in the measurement of sides is + 1%, and the error in the measurement of mass is + 2%, the maximum possible error in density is –**

- 1%
- 5%
- 3%
- 7%

**Answer:** 2. 1%

**Question 4. To estimate ‘g’ (from \(\mathrm{g}=4 \pi^2 \frac{\mathrm{L}}{\mathrm{T}^2}\) error in measurement of L is ± 2% and error in measurement of T is + 3%. The error in estimated ‘g’ will be**

- ± 8%
- ± 6%
- ± 3%
- ± 5%

**Answer:** 1. ± 8%

**Question 5. The least count of a stopwatch is 0.2 seconds. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The percentage error in the period is**

- 16%
- 0.8 %
- 1.8 %
- 8 %

**Answer:** 1. 16%

**Question 6. The dimensions of a rectangular block measured with vernier calipers having the least count of 0.1 mm are 5 mm × 10 mm × 5 mm. The maximum percentage error in the measurement of the volume of the block is**

- 5 %
- 10 %
- 15 %
- 20 %

**Answer:** 1. 5 %

**Question 7. An experiment measures quantities x, y, z, and then t is calculated from the data as \(t=\frac{x y^2}{z^3}\) If percentage errors in x, y, and z are respectively 1%, 3%, 2%, then percentage error in t is :**

- 10 %
- 4 %
- 7 %
- 13 %

**Answer:** 4. 13 %

**Question 8. The external and internal diameters of a hollow cylinder are measured to be (4.23 ± 0.01) cm and (3.89 ± 0.01) cm. The thickness of the wall of the cylinder is**

- (0.34 ± 0.02) cm
- (0.17 ± 0.02) cm
- (0.17 ± 0.01) cm
- (0.34 ± 0.01) cm

**Answer:** 3. (0.17 ± 0.01) cm

**Question 9. The mass of a ball is 1.76 kg. The mass of 25 such balls is**

- 0.44 × 103 kg
- 44.0 kg
- 44 kg
- 44.00 kg

**Answer:** 2. 44.0 kg

**Question 10. Two resistors R1 (24 ± 0.5) and R2 (8 ± 0.3) are joined in series. The equivalent resistance is**

- 32 ± 0.33 Ω
- 32 ± 0.8Ω
- 32 ± 0.2 Ω
- 32 ± 0.5 Ω

**Answer:** 2. 32 ± 0.8Ω

**Question 11. The pitch of a screw gauge is 0.5 mm and there are 100 divisions on its circular scale. The instrument reads +2 divisions when nothing is put in between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and 83rd division coincides with the reference line. Then the diameter of the wire is**

- 4.05 mm
- 4.405 mm
- 3.05 mm
- 1.25 mm

**Answer:** 2. 4.405 mm

**Question 12. The pitch of a screw gauge having 50 divisions on its circular scale is 1 mm. When the two jaws of the screw gauge are in contact with each other, the zero of the circular scale lies 6 divisions below the line of graduation. When a wire is placed between the jaws, 3 linear scale divisions are visible while the 31st division on the circular scale coincides with the reference line. The diameter of the wire is :**

- 3.62 mm
- 3.50 mm
- 3.5 mm
- 3.74 mm

**Answer:** 4. 3.74 mm

**Question 13. The smallest division on the main scale of vernier calipers is 1 mm, and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a sphere, the zero mark of the vernier scale lies between 2.0 and 2.1 cm and the fifth division of the vernier scale coincides with a scale division. The diameter of the sphere is**

- 2.05 cm
- 3.05 cm
- 2.50 cm
- None of these

**Answer:** 1. 2.05 cm

**Question 14. You are given two unknown resistors X and Y. These resistances are to be determined, using an ammeter of R A = 0.5 and a voltmeter of Rv = 20 k. It is known that X is in the range of a few ohms and Y is in the range of several kiloohms. Which circuit is preferable to measure X and Y: Resistor Circuit**

- x (a) y (b)
- x → (a), y → (b) x → (b), y → (a)
- x → (a), y → (a) x → (b), y → (b)

**Answer:** 2. x → (a), y → (b) x → (b), y → (a)

**Question 15. The main scale of the vernier calipers reads 10 mm in 10 divisions. 10 divisions of the Vernier scale coincide with 9 divisions of the main scale. When a cylinder is tightly placed between the two jaws, the zero of the vernier scale lies slightly behind 3.2 cm and the fourth vernier division coincides with a main scale division. The diameter of the cylinder is :**

- 3.09 cm
- 3.14 cm
- 3.04 cm
- 3.03 cm

**Answer:** 2. 3.14 cm

**Question 16. Two resistances are measured in Ohm.**

- R1 = 3Ω ± 1%
- R2 = 6Ω ± 2%

**When they are connected in parallel, the maximum percentage error in equivalent resistance is x. Find 3x.**

- 4
- 5
- 7
- 9

**Answer:** 1. 4

**Question 17. The edge of a cube is a = 1.2 10−2 m. Then its volume will be recorded as:**

- 1.72 x 10−6 m3
- 1.728 x 10−6 m3
- 1.7 x 10−6 m3
- 1.73 x 10−6 m3

**Answer:** 3. 1.7 x 10−6 m3

**Question 18. In the shown arrangement of the experiment of the meter bridge if the length AC corresponding to the null deflection of the galvanometer is x, what would be its value if the radius of the wire AB is doubled? **

- x
- x/4
- 4x
- 2x

**Answer:** 1. X

**Question 19. In the post office arrangement to determine the value of unknown resistance, the unknown resistance should be connected between:**

- B and C
- C and D
- A and D
- B1 and C

**Answer:** 3. A and D

**Question 20. A wire has a mass (0.3 ± 0.003)g, radius (0.5 ± 0.005)mm and length (6 ± 0.06)cm. The maximum percentage error in the measurement of its density is:**

- 1
- 2
- 3
- 4

**Answer:** 4. 4

**Question 21. A student experiments determination of \(\left(=\frac{4 \pi^2 \ell}{\mathrm{T}^2}\right), \ell \approx 1 \mathrm{~m}\), and he commits an error ****of Δl. For T he takes the time of n oscillations with the stopwatch of least count ΔT and he commits a human error of 0.1 sec. For which of the following data, the measurement of g will be most accurate?**

- ΔL = 0.5, ΔT = 0.1, n = 20
- ΔL = 0.5, ΔT = 0.1, n = 50
- ΔL = 0.5, ΔT = 0.01, n = 20
- ΔL = 0.1, ΔT = 0.05, n = 50

**Answer:** 4. ΔL = 0.1, ΔT = 0.05, n = 50

**Question 22. A resistance of 2 is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is**

- 3Ω
- 4Ω
- 5Ω
- 6Ω

**Answer:** 1. 3Ω

**Question 23. A vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is:**

- 0.02 mm
- 0.05 mm
- 0.1 mm
- 0.2 mm

**Answer:** 4. 0.2 mm

**Question 24. A meter bridge is set up as shown, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows a null point when the tapping key is at the 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is:**

- 10.2 ohm
- 10.6 ohm
- 10.8 ohm
- 11.1 ohm

**Answer:** 2. 10.6 ohm

**Question 25. Unit of diploe moment is:**

- -amp-m
- coulomb-m
- amp-m²
- coulomb-m²

**Answer:** 2. coulomb-m

**Question 26. The length, breadth, and thickness of a block are given by l = 12cm, b = 6 cm, and t = 2.45 cm. The volume of the block according to the idea of significant figures should be:**

- 1× 102 cm
_{3} - 2 × 102 cm
_{3} - 1.763 × 102 cm
_{3} - None of these

**Answer:** 2. 2 × 102 cm_{3}

**Question 27. An ice cube of density 900 kg/m 3 is floating in water of density 1000 kg/m 3. The percentage of the volume of ice-cube outside the water is:**

- 20%
- 35%
- 10%
- None of these

**Answer:** 3. 10%

**Question 28. In an experiment four quantities a, b, c, and d are measured with percentage errors 1%, 2%, 3%, and 4% respectively. Quantity P is calculated as follows :**

- 10%
- 7%
- 4%
- 14%

**Answer:** 4. 14%

**Question 29. An experiment measures quantities a, b, c, and x calculated from x = If the percentage errors in a, b, c are ± 1%, ± 3%, and ± 2% respectively.**

- The percentage error in x can be ± 13%
- The percentage error in x can be ± 30%
- The percentage error in x can be ± 20%
- The percentage error in x can be ± 26%

**Answer:** 1. The percentage error in x can be ± 13%

**Question 30. If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be**

- 4%
- 6%
- 8%
- 2%

**Answer:** 2. 6%

**Exercise- 2**

**Question 1. The number of circular divisions on the shown screw gauge is 50. It moves 0.5 mm on the main scale for one complete rotation. The main scale reading is 2. The diameter of the ball is:**

- 2.25 mm
- 2.20 mm
- 1.20 mm
- 1.25 mm

**Answer:** 3. 1.20 mm

**Question 2. A student experiments to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ±0.01 mm. Take g = 9.8 m/s _{2} (exact). The Young’s modulus obtained from the reading is**

- (2.0 ± 0.3) × 1011 N/m
_{2} - (2.0 ± 0.2) × 1011 N/m
_{2} - (2.0 ± 0.1) × 1011 N/m
_{2} - (2.0 ± 0.05) × 1011 N/m
_{2}

**Answer:** 2. (2.0 ± 0.2) × 1011 N/m2_{2}

**Question 3. Students 1, 2, and 3 experiment with measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and /or record time for different numbers of oscillations. The observations are shown in the table. Least count for length = 0.1 cm Least count for time = 0.1 s If Eg 100 1, E2and E3 are the percentage errors in g, i.e., for students 1 2, and 3, respectively,**

- E1 = 0
- E1 is minimum
- E1 = E2
- E2 is maximum

**Answer:** 2. E1 is minimum

**Question 4. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is**

- 0.9%
- 2.4%
- 3.1%
- 4.2%

**Answer:** 3. 3.1%

**Question 5. Consider vernier calipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the vernier calipers, 5 divisions of the vernier scale coincide with 4 divisions on the main scale, and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then,**

- If the pitch of the screw gauge is twice the least count of the Vernier calipers, the least count of the screw gauge is 0.01mm.
- If the pitch of the screw gauge is twice the least count of the Vernier calipers, the least count of the screw gauge is 0.005mm.
- If the least count of the linear scale of the screw gauge is twice the least count of the vernier calipers, the least count of the screw gauge is 0.005 mm.
- None of these

**Answer:** 2. If the pitch of the screw gauge is twice the least count of the Vernier calipers, the least count of the screw gauge is 0.005mm.

**Question 6. The energy of a system as a function of time t is given as E(t) = A2 exp(–at), where a = 0.2s–1. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 s is**

- 1
- 2
- 3
- 4

**Answer:** 4. 4

**Question 7. A body of uniform cross-sectional area floats in a liquid of density thrice its value. The fraction of exposed height will be:**

- 2/3
- 5/6
- 1/6
- 1/3

**Answer:** 1. 2/3

**Question 8. A meter bridge is used to find the resistance of a wire using a standard resistance 20 with 0.5% tolerance. The unknown resistance is placed in the left gap of the meter bridge. The null point is obtained at 60.0 cm from the left end. The maximum permissible error in this measurement is 0.1 cm. Find the maximum error in the measurement of the resistance.**

- 0.37Ω
- 0.35Ω
- 0.20Ω
- 0.27Ω

**Answer:** 4. 0.27Ω

**Question 9. Two full turns of the circular scale of a screw gauge cover a distance of 1mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of –0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is:**

- 3.32 mm
- 3.73 mm
- 3.67 mm
- 3.38 mm

**Answer:** 4. 3.38 mm

**Question 10. An experiment is performed to find the refractive index of glass using a traveling microscope. In this experiment, distance is measured by**

- A vernier scale provided on the microscope
- A standard laboratory scale
- A metal scale provided on the microscope
- A screw gauge provided on the microscope

**Answer:** 1. A vernier scale provided on the microscope

## Chapter 2 Measurement Errors And Experiments MCQs Part – 1: Neet / Aipmt Question (Previous Years)

**Question 1. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are e 1 and e2 respectively, the percentage error in the estimation of g is**

- e
_{2}– e_{1} - e
_{1 }+ 2e_{2} - e
_{1}+ e - e
_{1}– 2e_{2}

**Answer:** 2. e_{1} + 2e_{2}

**Question 2. In an experiment, the percentage of error that occurred in the measurement of physical quantities A, B, C, and D are 1%, 2%, 3%, and 4% respectively. Then the maximum percentage of error in the measurement X, where X = \(X=\frac{A^2 B^{1 / 2}}{C^{1 / 3} D^3}\) will be**

- 10%
- \(\left(\frac{3}{13}\right) \%\)
- 16%
- 10%

**Answer:** 3. \(\left(\frac{3}{13}\right) \%\)

**Question 3. The main scale of vernier calipers has n divisions/cm. n division of the vernier scale coincides with (n – 1) divisions of the main scale. The least count of the vernier calipers is :**

- \(\frac{1}{(n+1)(n-1)} c m\)
- \(\frac{1}{\mathrm{n}} \mathrm{cm}\)
- \(\frac{1}{\mathrm{n}^2} \mathrm{~cm}\)
- \(\frac{1}{n(n+1)} \mathrm{cm}\)

**Answer:** 3. \(\frac{1}{\mathrm{n}^2} \mathrm{~cm}\)

## Chapter 2 Measurement Errors And Experiments MCQs Part – 2: Jee (Main) / AIEEE Problems (Previous Years)

**Question 1. In an experiment, the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree ( 0.5°), then the least count of the instrument is:**

- Half minute
- One degree
- Half degree
- One minute

**Answer:** 4. One minute

**Question 2. In an optics experiment, with the position of the object fixed, a student varies the position of the convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45° with the x-axis meets the experimental curve at P. The coordinates of P will be:**

- \(\left(\frac{\mathrm{f}}{2}, \frac{\mathrm{f}}{2}\right)\)
- (f, f)
- (4f, 4f)
- (2f, 2f)

**Answer:** 4. (2f, 2f)

**Question 3. The respective number of significant figures for the numbers 23.023, 0.0003, and 2.1 × 10–3 are**

- 5, 1, 2
- 5, 1, 5
- 5, 5, 2
- 4, 4, 2

**Answer:** 1. 5, 1, 2

**Question 4. 4. A screw gauge gives the following reading when used to measure the diameter of a wire.**

- Main scale reading : 0 mm
- Circular scale reading: 52 division
- Given that 1 mm on the main scale corresponds to 100 divisions of the circular scale.

**The diameter of the wire from the above data is:**

- 0.52 cm
- 0.052 cm
- 0.026 cm
- 0.005 cm

**Answer:** 2. 0.052 cm

**Question 5. If 400Ω of resistance is made by adding four 100 Ω resistances of tolerance 5%, then the tolerance of the combination is:**

- 5%
- 10 %
- 15 %
- 20 %

**Answer:** 1. 5%

**Question 6. The period of oscillation of a simple pendulum is T = 2g. The measured value of L is 20.0 cm known as 1 mm accuracy and the time for 100 oscillations of the pendulum is found to be 90s using a wristwatch of 1s resolution. The accuracy in the determination of g is:**

- 2%
- 3%
- 1%
- 5%

**Answer:** 2. 3%

**Question 7. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:**

- 4.5%
- 6%
- 2.5%
- 3.5 %

**Answer:** 1. 4.5%

**Question 8. The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet are 5.5 mm and 48 respectively, the thickness of this sheet is :**

- 5.740 mm
- 5.950 mm
- 5.725 mm
- 5.755 mm

**Answer:** 4. 5.755 mm

**Question 9. Expression for time in terms of G (universal gravitational constant), h (Planck constant), and c (speed of light) is proportional to:**

- \(\sqrt{\frac{h c^5}{G}}\)
- \(\sqrt{\frac{\mathrm{Gh}}{\mathrm{c}^3}}\)
- \(\sqrt{\frac{\mathrm{Gh}}{\mathrm{c}^3}}\)
- \(\sqrt{\frac{\mathrm{Gh}}{\mathrm{c}^3}}\)

**Answer:** 4. \(\sqrt{\frac{\mathrm{Gh}}{\mathrm{c}^3}}\)

**Question 10. The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in the appropriate significant figure?**

- 4264 ± 81 cm³
- 4300 ± 80 cm³
- 4260 ± 80 cm³
- 4264.4 ± 81.0 cm³

**Answer:** 3. 4260 ± 80 cm

**Question 11. The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure the 5m diameter of a wire is:**

- 200
- 50
- 500
- 100

**Answer:** 1. 200

**Question 12. In a simple pendulum experiment for the determination of acceleration due to gravity (g), the time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 seconds. The length of the pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:**

- 0.2%
- 0.7%
- 6.8 %
- 3.5 %

**Answer:** 3. 6.8 %

**Question 13. In the density measurement of a cube, the mass and edge length are measured as (10.00 0.10) kg and (0.10 0.01) m, respectively. The error in the measurement of density is:**

- 0.07 kg/m³
- 0.10 kg/m³
- 0.01 kg/m³
- 0.31 kg/m³

**Answer:** 4. 0.31 kg/m³

**Question 14. The area of a square is 5.29 cm². The area of 7 such squares taking into account the significant figures is:**

- 37.0 cm²
- 37 cm²
- 37.03 cm²
- 37.030 cm²

**Answer:** 3. 37.03 cm²