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Objective Type, 1., , ¥, , 10., , 11., , 13., , 14., , . The percentage error in measuring the diameter of a ball by screw gauge is 2.0% . The error in, , . Mass of a piece of gold is given as 10 mg. Maximum error in its measurement should be :, , (a) 2% (b) 4% (c) 6% (d) 8%. (UPB 2012), . The error in the measurement of volume of a cube is 9%. The error in the surface area of the cube, , will be :, , (a) 3% (b) 6% (c) 12% (a) 18%. (UPB 2008), , Rees see, , The diameter of a wire is measured 0.236 cm by a screw gauge. If the least count of screw Bauge, 0.001 cm, then the probable percentage of error in this measurement will be : , (a) 0,001 (b) 0.42 (c) 0.236 (d) 0.237., , calculation of volume of the ball will be :, (a) 1.5% (b) 6.0% (c) 4.0% (d) 2.0%., , There is an error of 3% in the measurement of a side of a square. The error in the calculation of its, area will be :, , (a) 6% (b) 3% (c) 9% (d) 1.5%. (UPB 2009), There is an error of 2% in the measurement of side of a cube. The percentage error in the calculation, of its volume will be :, , (a) 1% (b) 2% (c) 3% (d) 6%. (UPB 2014, 12), The error in the measurement of radius of a sphere is 3%. Then, the error in the calculation of, volume of the sphere will be :, , (a) 3% (b) 6% (c) 9% (d) 1%. (UPB 2012), The error in the measurement of radius of a sphere is 0.25%. The error in the calculation of the, volume of the sphere will be :, , (a) 0.25% (b) 0.50% (c) 0.75% (d) 1.00% ., , The length of a cylinder is 10.0 cm and its radius is 4.00 cm. The per cent error in the volume of the, cylinder will be :, , (a) 1.5% (b) 2.0% (c) 3.5% (d) 10.7%., , (a) 0.01% (b) 0.1% (c) 1.0% (d) 10.0%. (UPB 2012), A glass plate is of length 2.0 cm and width 1.5 cm. The maximum probable error in measuring the, area of the plate is :, , (a) 0.15 cm? (b) 0.25 cm? (c) 0.35 cm? (d) 0.45 em?., , The percentage error in the measurements of radius of a circular plate and force applied on it are, 1% and 2% respectively. The maximum percentage error in the pressure exerted on the plate is :, (a) 2% (b) 3% (c) 4% (d) 5%. (UPB 2011), The maximum percentage error in finding the volume of a sphere is 6%. The maximum percentage, error in finding its surface area will be :, , ‘The error in the measurements of mass and volume of a solid are 5% and 2% respectively. The, maximum percentage error in the measurement of its density will be : 4, (a) 10 (b) 25 (c)7 (d) 3. (UPB 201, The errors in measurement of mass and radius are 2% and 3% respectively of a spherical block. The, maximum percentage error in calculation of density of the material of the block will be :, , (a) 5% ae © 6% (a) 11%. (UPB 2015), , , , Ln

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UNITS, MEASUREMENTS AND ERROR ANALYSIS. 45, , 15, The percentage errors in the measurements of mass and speed of a body are 2% and 3% respectively., The maximum percentage error in the estimate of kinetic energy of the body will be :, () 2% (b) 3% (c) 8% (d) 5%., (UPB 2013, 12, 08), 16. The error in'the measurement of the radius of a sphere is 3.0%, and in the measurement of mass is, 2.0%. The maximum error in the calculation of density of the substance of the sphere will be :, (a) 5.0% (b) 1.0% (c) 11.0% (d) 7.0%,, , 17. The speed of wave in a stretched string is represented by v = JT/m. If the error in the measurement, , of tension T is 2% and in the measurement of mass per unit length m is 3%, then the maximum, error in the calculation of speed will be ;, , (a) 5.0% (b) 1,0% (c) 2.5% (d) 0.5%., , 18. In the simple pendulum experiment, the error in measurement of the length of the pendulum is 2%, , and error in measurement of time-period is 3%. The maximum percentage error in the measurement, of value of g will be :, , (a) 5% (b) 6% (c) 1.5% (d) 8%. (UPB 2014), 19. Time of 10 oscillations measured by stop-clock of a simple pendulum of length 1.0 metre is, , L, 20 seconds. Least-count of the stop-clock is 0.1 second. In calculation of $ = 4n? Pr , the percentage, , error of g will be :, (a) 1% (b) 10% (c) 11% (d) 20%. (UPB 2015), , Hint. 48 x 100 = 29% x 100 = 2x 94 x 100 = 1%, g t 20, , 20. Ifv=d/twithd=10mandt=S5s, then find maximum probable percentage error in the determination, of uv. Least counts of the measurements of d and ¢ are 1 cm and 1s respectively :, , (a) 19.9 (b) 20.1 (c) 20.0 (d) 10.1., , 21. Astudent measures quantities a, b and c then calculates S by the formula S = ab?/c>. If the errors in, a, b, care 1%, 3% and 2% respectively, the maximum error in S can be :, , (a) 13% (b) 7% (c) 4% (d) 1%., , 22. The amount of heat produced in an electric circuit depends upon the current i, resistance R and time, t, according to relation H = i? Re. If errors in measuring i, R and t are 2%, 1% and 1% respectively,, the maximum error in the computed value of H will be:, , (a) 4% (b) 6% (©) 8% (d) 2%., , m, 23, In a physical quantity Y = 7 , the errors in the measurements of a and b are x and y. Maximum, , error in calculating Y will be :, , (a) mx + ny (b) mx~ ny (Oirexseny (4) mx/ny. (UPB 2014), 24, The following equation is used for measuring a physical quantity Y ;, 2, y=4 ob, 3.3, , Here, a = 4.0, b = 1.00 and c = 3.000. The per cent error in Measuring Y will be : :, (a) 2.3% (b) 4.6% (6.5% (d) 11.7%. (UPB 2008)

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RRS SETS rE Nae, , 0 + 0.3)°C. The maximy,, , , , (20.0 + 0.2 )°C to (25:, , 46, : e becomes from :, 25. On heating water its temperaru? f water will be : ., eed error in i oO! (c) (10/9)% (d) (2/9)%. (UPB 2015,, 2% i :, 26 ae 07200, number of significant figures willbe (4 (d) 5.° (UPB 2016), ie (b) 3, (a) 2, ANSWERS, maar et le SE aS See 6, a ce le 6G Oe Oe ee, 21. (@) 22.0) 23.2) 2% @) 25.0) 26 &:, Very Short-Answer Type, , 1. What is the average distance of sun from earth? o, Ans. 1 astronomical unit (AU), that is, 1.496 x 10°" m., 2. Are there more microseconds in a second than number of seconds in a year?, Ans. No, these figures are 10° and 3.15 x 10” respectively., 3. Are there more shakes in a second than seconds in a year?, Ans. Yes., 4. How much longer is a millisecond than a microsecond?, Ans, 10° times., 5, What is meant by torr?, Ans. It is the unit of pressure. 1 torr is the pressure due to 1 mm of mercury column., 6. Express 0.000003 kg in power of 10., Ans. 3 x 107° kg., 7. Is the measure of an angle dependent upon the unit of length?, , Ans. No. ', 8. What is the order of size of our galaxy and that of the height of an average man? Of mean free path, of an air molecule? co, Ans. 107° m, 10° m, 107° m. ee, 9, What does RADAR stand for? >, Ans. Radio Detection And Ranging., 10. What is a LASER beam? ie, Ans. It is a very intense, highly monochromatic and unidirectional beam of li, 11. What is meant by SONAR? What type of waves,are used in it? “dee, Ans. SONAR means sound navigation and ranging. It uses ultrasonic wayes,, 12. What are significant figures? tee, (UPB 2015), 13. Is the digit 0 in a number significant? Explain., Ans. 0 is significant if it falls between two'significant digits (as in 60.5 “, measurement (as in 6.50 cm). It is insignificant if it fixes the position of ota fine ind ee, 14. State the number of significant figures in the followings : . ;, (i) 0.050 cm, (ii) 0.0009 m, (iii) 0.039 m, (iv) 6.37 x 10° m, (vy) 2, i <i Li cogi : 0.009203 m’,, (vi) 1.99 x 10°° kg, (vii) 9.1 x 1077! kg, (viliy’3.08 x 10° s, (ix) 2.99 x 10°ms™7, @ 1,60x 10779., Ans. (i) two, (ii) one, (iii) two, (iv) three, (v) four, (vi) three, (vii) two, (viii) three, (x) three,, , (x) three.

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UNITS, MEASUREMENTS AND ERROR ANALYSIS, 15., , 16., , 17., , 18., , 19., , 20., , 21., , 47, Which of the following measured lengths is most accurate and why?, (i) 3.0 cm, (ii) 3.00 cm, (iii) 3.000 cm., , Ans. 3.000 cm is most accurate because it has maximum number of significant figures (four)., The mass of a body measured by three persons was expressed as, , (i) 2000 g, (ii) 2.00 kg, (iii) 2.0 x 10° g., , Which one expresses the most accurate measurement and why?, , Ans. 2000 g is most accurate, because it has maximum (four) significant figures., What is the difference between the length measurements 2.0 cm and 2.000 cm?, , Ans. 2.0 cm indicates that the measurement is accurate up to first decimal place only, while the, measurement 2.000 cm is accurate up to third decimal place., , If f= x, then how many times is the fractional error in f than the fractional error in x?, , Ans. Two times ; # or, f x, , Which quantity in a given formula should be measured maximum accurate?, , Ans. The quantity occurring in highest power, say n, should be measured with maximum accuracy, because any error in the measurement of this quantity is magnified n times in the final result., Maximum error of 4% occurs in the measurement of surface area of a sphere. What will be the, maximum error in the measurement of its volume? (UPB 2016), , Ans. 6%., , Round off the following to three significant figures :, (i) 1.0084, (ii) 36.99, (iii) 0.005135, (iv) 6.225, (v) 0.03828, (vi) 3.15360 x 10”., Ans. (i) 1.01, (ii) 37.0, (iii) 0.00514, (iv) 6.22, (v) 0.0383, (vi) 3.15 x 10”.