MEASUREMENT ERROR & EXPERIMENT Exercise # 4 [Subjective Type Questions] 1. Consider a home made vernier scale as shown in the figure. In this diagram, we are interested in measuring the length of the line PQ. If both the inclines are identical and their angles are equal to q then what is the least count of the instrument. 2. In a given slide callipers 10 division of its vernier coincides with its 9 main scale divisions. If one main scale division is equal to 0.5 mm then find its least count. 3. The pitch of a screw gauge is l mm and there are 50 divisions on its cap. When nothing is put in between the studs, 44th division of the circular scale coincides with the reference line zero of the main scale is not visible. When a glass plate is placed between the studs, the main scale reads three divisions and the circular scale reads 26 divisions. Calculate the thickness of the plate. 4. A glass prism of angle A = 60° gives minimum angle of deviation q = 30° with the maximum error of 1° when a beam of parallel light passed through the prism during an experiment. Find the permissible error in the measurement of refractive index m of the material of the prism. 5. A short circuit occurs in a telephone cable having a resistance of 0.45 Wm-1 . The circuit is tested with a Wheatstone bridge. The two resistors in the ratio arms of the Wheatstone bridge network have values of 100W and 1110 W respectively. A balance condition is found when the variable resistor has a value of 400W. Calculate the distance down the cable, where the short has occurred. 6. In a given optical bench, a needle of length 10 cm is used to estimate bench error. The object needle, image needle & lens holder have their reading as shown. x0 = 1.1 cm; x1 = 0.8 cm; xL = 10.9 cm Estimate the bench errors which are present in image needle holder and object needle holder. Also find the focal length of the convex lens when x0 = 0.6 cm ; xI = 22.5 cm; xL = 11.4 cm Consider S = x cos (q) for x = (2.0 ± 0.2) cm, q = 53 ± 2°. Find S. 7. 8. Using screw gauge, the observation of the diameter of a wire are 1.324, 1.326, 1.334, 1.336 cm respectively. Find the average diameter, the mean error, the relative error and % error. Find significant figures in the following observations (i) 0.007 gm (ii) 2.64 x 1024 kg (iii) 0.2370 gm/cm3 (iv) 6.320 J/K 2 –1 (v) 6.032 N/m (vi) 0.0006032 K 9. 10. If a tuning fork of frequency (f0) 340 Hz and tolerance  1% is used in resonance column method [v = 2f0 (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. 11. Round off the following numbers within three significant figures (i) 0.03927 kg (ii) 4.085 x 108 sec (iii) 5.2354 m (iv) 4.735 x 10–6 kg EXERCISE - 4 1. 1  cos   LC  l   cos   6. D  1.330 cm , D  0.005 cm , Relative error = + 0.004 %, error = 0.4% 7. 8. 5.5 ± 0.05 cm (vi) 4 11. (i) 0.0393 kg 9. 2. (i) 1 0.05 mm (ii) 3 (ii) 4.08 x 108 sec 3. Rt = 3.64 mm (iii) 4 (iv) 4 4. 5 % 18 (v) 4 (iii) 5.24 m (iv) 4.74 x 10–6 kg 5. 40m S = (1.2 ± 0.18) cm 10. 1.4%