Measurement Error & Experiment Exercise # 1

MEASUREMENT ERROR & EXPERIMENT Exercise # 1 [Single Correct Choice Type Questions] 1. The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed ? (A) 11% (B) 8% (C) 5% (D) 1% 2. Significant figures in 3400 are(A) 2 (B) 5 (C) 6 (D) 7 3. The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of the density is (A) 9% (B) 13% (C) 12% (D) 7% 4. If error in measuring diameter of a circle is 4%, the error in the radius of the circle would be (A) 2% (B) 8% (C) 4% (D) 1% 5. An experiment measures quantities a, b and c, and X is calculated from X = c are ±1%, ±3% and ±2% respectively, the percentage error in X will be – (A) ±13% (B) ±7% (C) ±4% ab 2 . If the percentage error in a, b and c3 (D) ±1% 6. While measuring acceleration due to gravity by a simple pendulum a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of the time period. His percentage error in the measurement of the value of g will be (A) 2% (B) 4% (C) 7% (D) 10% 7. The diameter of a wire is measured with a screw gauze having least count 0.01 mm. Which of the following correctly expresses the diameter – (A) 0.20 cm (B) 0.002 m (C) 2.00 mm (D) 0.2 cm 8. If a, b, c are the percentage errors in the measurement of A, B and C, then percentage error in ABC would be approximately(A) abc (B) a + b + c (C) ab + bc + ac (D) a b c   b c a 9. A student measured the diameter of a wire using a screw gauge with least count 0.001 cm and listed the measurements. The correct measurement is – (A) 5.3 cm (B) 5.32 cm (C) 5.320 cm (D) 5.3200 cm 10. The period of oscillation of a simple pendulum in the experiment is recorded as 2.63s, 2.56s, 2.42s, 2.71s and 2.80s respectively. The average absolute error is (A) 0.1s (B) 0.11s (C) 0.01s (D) 1.0s The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, the maximum error in the measurement of pressure is – (A) 1% (B) 2% (C) 6% (D) 8% When a copper sphere is heated, maximum percentage change will be observed in– (A) radius (B) area (C) volume (D) none of these 11. 12. 13. A scientist performs an experiment in order to measure a certain physical quantity and takes 100 observations. He repeats the same experiment and takes 400 observations, by doing so (A) The possible error remains same (B) The possible error is doubled (C) The possible error is halved (D) The possible error is reduced to one fourth 14. The significant digits in 200.40 are (A) 4 (B) 5 (C) 2 (D) 3 15. If error in measuring diameter of a circle is 4 %, the error in circumference of the circle would be :(A) 2% (B) 8% (C) 4% (D) 1% 16. A quantity is represented by X = Ma Lb Tc. The percentage error in measurement of M, L and T are %, % and  % respectively. The percentage error in X would be (A) (a + b + c) % (B) (a – b + c) % (C) (a – b– c) % (D) None of these 17. 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 – (A) 1 (B) 2 (C) 3 (D) 4 18. The volume of a sphere is 1.76 cm . The volume of 25 such spheres taking into account the significant figure is2 3 3 3 3 (A) 0.44 × 10 cm (B) 44.0 cm (C) 44 cm (D) 44.00 cm 19. The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier callipers having least count 0.01 cm. Given the length is 5.0 cm and diameter is 2.00 cm. The percentage error in the calculated value of volume will be – (A) 2% (B) 1% (C) 3% (D) 4% 20. The resistance is R  V where V = 100 ± 5 Volts and I = 10 ± 0.2 amperes. What is the total error in R ? I 5 (A) 5% (B) 7% (C) 5.2% (D)   % 2 21. What is the fractional error in g calculated from T  2  3 y respectively. (A) x + y (B) x – y l ? Given that fractional errors in T and  are ± x and ± g (C) 2x + y (D) 2x – y) 22. The external and internal radius 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 :(A) (0.34 ± 0.02)cm (B) (0.17 ± 0.02)cm (C) (0.17 ± 0.01)cm (D) (0.34 ± 0.01)cm 23. The length, breadth and thickness of a strip are (10.0 ± 0.1)cm, (1.00 ± 0.01) cm and (0.100 ± 0.001) cm respectively. The most probable error in its volume will be (A) ± 0.03 cm3 (B) ± 0.111 cm3 (C) ± 0.012 cm3 (D) none of these 24. The length , breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are = 15.12  0.01 cm, b = 10.15  0.01 cm, t = 5.28  0.01 cm. The percentage error in volume upto proper significant figures is – (A) 0.28% (B) 0.36% (C) 0.48 % (D) 0.64% 25. The radius of a disc is 1.2 cm. Its area according to idea of significant figures, will be given by:2 2 2 2 (A) 4.5216 cm (B) 4.521 cm (C) 4.52 cm (D) 4.5 cm 26. The following observations were taken for determining surface tension of water by capillary tube method: –2 –2 2 Diameter of capillary D = 1.25 × 10 m Rise of water in capillary, h = 1.45 × 10 m. Taking g = 9.80 m/s and 3 using the relation T = (rhg/2) × 10 N/m, what is the possible error in surface tension. T– (A) 0.16% (B) 1.6% (C) 16% (D) 2.4% MEASUREMENT ERROR & EXPERIMENT 27. The area of a rectangle of size 1.23 × 2.345 cm is (A) 2.88 cm2 (B) 2.884 cm2 (C) 2.9 cm2 (C) 2.88435 cm2 28. The least count of a stop watch is 1/5 sec. The time of 20 oscillations of a pendulum is measured to be 25 s. What is the maximum percentage error in this measurement (A) 8% (B) 1% (C) 0.8% (D) 16% 29. The vernier of a circular scale is divided into 30 divisions which coincide against 29 divisions of main scale. Each main scale division is 0.5°. The least count of the instrument is – (A) 10' (B) 0.1' (C) 1' (D) 30' 30. What is vernier constant (A) It is the value of the one main scale division by the total number of divisions on the main scale. (B) It is the value of one vernier scale division divided by the total number of division on the vernier scale. (C) It is the difference between value of one main scale division and one vernier scale division (D) It is not the least count of vernier scale. 31. A vernier callipers having 1 main scale division = 0.1 cm is designed to have a least count of 0.02 cm. If n be the number of divisions on vernier scale and m be the length of vernier scale, then (A) n= 10, m = 0.5 cm (B) n=9, m= 0.4 cm (C) n=10, m = 0.8 cm (D) n=10, m= 0.2 cm 32. What is the reading of micrometer screw gauge shown in figure (A) 2.30 mm 33. (C) 2.36 mm 35 30 25 (D) 2.41 mm In a vernier calliper, N divisions of vernier scale coincide with (N – 1) divisions of main scale (in which 1 division represents 1mm). The least count of the instrument in cm. should be 1 1 (D) 1 0N N 1 In a vernier callipers the main scale and the vernier scale are made up different materials. When the room temperature increases by T°C, it is found the reading of the instrument remains the same. Earlier it was observed that the front edge of the wooden rod placed for measurement crossed the Nth main scale division and N+2 MSD coincided with the 2nd VSD. Initially, 10 VSD coincided with 9 MSD. If coefficient of linear expansion of the main scale is 1 and that of the vernier scale is 2 then what is the value of 2? (Ignore the expansion of the rod on heating) (A) 1.8 /N (B) 1.8/ (N+3.8) (C) 1.8/ (N–2) (D) 1.8/N+2 (A) N 34. (B) 2.29 mm 0 1 2 mm (B) N – 1 (C) 35. In a vernier callipers, N divisions of the main scale coincide with N+m divisions of the vernier scale. What is the value of m for which the instrument has minimum least count? (A) 1 (B) N (C) infinity (D) N/2 36. For a post office box, the graph of galvanometer deflection versus R (resistance pulled out of RB) for the ratio 100 : 1 is given as shown. A careless student pulls out two non consecutive values R marked in the graph. Find the value of unknown resistance Deflection (in division) 5 326 -3 (A) 3.2 ohm (B) 3.24 ohm 320 R (C) 3.206 ohm (D) None 37. Consider the MB shown in the diagram, let the resistance X have temperature coefficient 1 and the resistance from the RB have the temperature coefficient 2. Let the reading of the meter scale be 10 cm from the LHS. If the temperature of the two resistance increase by small temperature T then what is the shift in the position of the null point? Neglect all the other changes in the bridge due to temperature rise (A) 9(1 - 2)T (B) 9 (1 + 2)T (C) 1/9 (1 + 2)T (D) 1/9 (1 - 2)T 38. In a meter bridge set up, which of the following should be the properties of the one meter long wire? (A) High resistivity and low temperature coefficient (B) Low resistivity and low temperature coefficient (C) low resistivity and high temperature coefficient (D) High resistivity and high temperature coefficient 39. Identify which of the following diagrams represent the internal construction of the coils wound in a resistance box or PO box ? P P (A) (B) P P (C) (D) EXERCISE - 1 1. B 14. B 27. A 2. A 15. C 28. C 3. B 16. A 29. C 4. C 17. D 30. C 5. A 18. D 31. C 6. C 19. C 32. A 7. C 20. B 33. C 8. B 21. C 34. B 9. C 22. A 35. A 10. B 23. A 36. B 11. D 24. B 37. A 12. C 25. D 38. A 13. D 26. B 39. D