Measurement Error & Experiment Exercise # 3

MEASUREMENT ERROR & EXPERIMENT Exercise # 3 1. [Matrix Match Type Questions] Part # I Match the columns. Column I i Backlash error ii Zero error iii Vernier callipers iv Error in screw gauge A B C D Column II Always subtracted Least count = 1 MSD – 1 VSD May be negative or positive Due to loose fitting 2. There are four vernier scales, whose specification are given in Column I and the least count is given in Column II. Match the Columns I and II with correct specification and corresponding least count (s = value of main scale division, n = number of marks on vernier). Assume (n – 1) main scale divisions are equal to n vernier divisions. Column I Column II i s = 1 mm , n = 10 A 0.05 mm ii s = 0.5 mm, n = 10 B 0.01 mm iii s = 0.5 mm, n = 20 C 0.1 mm iv s = 1 mm, n = 100 D 0.025 mm 3. Using significant figures, match the following Column I i 0.12345 ii 0.12100 cm iii 47.23  2.3 iv 3 × 108 Part # II A B C D Column II 5 4 1 2 [Comprehension Type Questions] Comprehension # 1 In the, Ohm’s law experiment, to find resistance of unknown resistor R, following two arrangements (A) and (B) are possible. A A v (a) The resistance measured is given by v (b) V i V = voltage reading of voltmeter, i = current Reading of ammeter. But unfortunately the ammeters and voltmeter used are not ideal, but having resistance RA and Rv respectively. R measured  1. For arrangement (A), the measured resistance is (A) R + Rv 2. (B) R + RA RR v (C) R  R v RR v (D) R  R  R A v RR v (C) R  R v RR v (D) R  R  R A v For arrangement (B), the measured resistance is (A) R + Rv (B) R + RA 3. You are given two unknown resistors X and Y. These resistances are to be determined, using an ammeter of RA = 0.5 W and a voltmeter of Rv = 20 kW. It is known that X is in range of a few ohms and Y is in the range of several kilo ohm's. Which circuit is preferable to measure X and Y : Resistor Circuit x (A) y (B) (A) x  (A), y  (B) (B) x  (B), y  (A) (C) x  (A), y  (A) (D) x  (B), y  (B) Comprehension # 2 Internal micrometer is a measuring instrument used to measure internal diameter (ID) of a large cylinder bore with high accuracy. Construction is shown in figure. There is one fixed rod B (to the right in figure) and one moving rod A (to the left in figure). It is based on the principle of advancement of a screw when it is rotated in a nut with internal threads. Main scale reading can be directly seen on the hub which is fixed with respect to rod B. When the cap is rotated, rod A moves in or out depending on direction of rotation. The circular scale reading is seen by checking which division of circular scale coincides with the reference line. This is to be multiplied by LC to get circular scale reading. Least count = value of 1 circular scale division  pitch number of division on circular scale Length of rod A is chosen to match the ID (PQ) to be measured. Zero error is checked by taking reading between standard blocks fixed at nominal value of ID to be measured. Zero error is positive if cap end is on the right side of the main scale and negative it is on the left side. Zero error checking Standard blocks 1. In an internal micrometer, main scale division is of 0.5 mm and there are 50 divisions in circular scale. The least count of the instrument is (A) 0.005 mm (B) 0.001 mm (C) 0.05 mm (D) 0.01 mm 2. In the above instrument, while measuring an internal diameter. ID is set of 321 mm with no zero error. If cap end is after 7th division and 17th division of main scale coincides with the reference line, the ID is(A) 321. 717 mm (B) 321.87 mm (C) 328.17 mm (D) 324.67 mm 3. During zero setting of the above instrument, the end of the cap is on left side of the zero of main scale (i.e. zero of main scale is not visible) and 41st division of circular scale coincides with the reference line, the zero error is(A) –0.09 mm (B) +0.41 mm (C) –0.41 mm (D) +0.09 mm EXERCISE - 3 : PART # I 1. i  D ; ii.  A,C iii.  B, iv  C, D 2. i  C, ii.  A, iii.  D, iv  B. 3. i  A ; ii.  A ; iii.  D; iv  C. PART # II Comprehension #1: 1. B 2. C 3. B Comprehension #2: 1. D 2. D 3. A