Exercise # 5 Part # I [Previous Year Questions] [MAIN] 1. The 'rad' is the correct unit used to report the measurement of : (1) the ability of a beam of gamma ray photons to produce ions in a target (2) the energy delivered by radiation to a target (3) the biological effect of radiation (4) the rate of decay of a radioactive source 2. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are meausred by (1) a vernier scale provided on the microscope (2) a stanard laboratory scale (3) a meter scale provided on the microscope (4) a screw gauge provided on the microscope 3. Two full turns of the circular scale of gauge cover a diastance of 1 mm on scale. The total number of divisions on circular scale is 50. Further, it is found that 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 division in line, with the main scale as 35. The diameter of the wire is (1) 3.32 mm (2) 3.73 mm (3) 3.67 mm (4) 3.38 mm 4. 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 :(1) One degree (2) Half degree (3) One minute (4) Half minute 5. In an optics experiment, with the position of the object fixed, a student varies the position of a 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 (1) (ƒ, ƒ) (2) (4ƒ, 4ƒ) (3) (2ƒ, 2ƒ) ƒ ƒ (4)  ,  2 2  6. The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10 –3 are:(1) 4, 4, 2 (2) 5, 1, 2 (3) 5, 1, 5 (4) 5, 5, 2 7. 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 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is :(1) 0.026 cm (2) 0.005 cm (3) 0.52 cm (4) 0.052 cm 8. A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data : (1) 59 degree (2) 58.59 degree (3) 58.77 degree (4) 58.65 degree 9. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is :(1) 3% (2) 6% (3) zero (4) 1% MEASUREMENT ERROR & EXPERIMENT 10. The current voltage relation of diode is given by I =  e1000V/T  1 mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring  0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ? (1) 0.5 mA 11. (2) 0.05 mA (3) 0.2 mA (4) 0.02 mA A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it? (1) A screw gauge having 100 divisions in the circular scale and pitch as 1 mm. (2) A screw gauge having 50 divisions in the circular scale and pitch as 1 mm. (3) A meter scale. (4) A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in 1 cm. 12. Match List-I (fundamental Experiment) with List –II (its conclusion) and select the correct option from the choice given below the list: List–I (A) Franck–Hertz List–II (i) Experiment (B) Photo-electric Experiment light (ii) experiment (C) Davison-Germer Particle nature of Discrete energy levels of atom (iii) Experiment. Wave nature of electron (iv) Structure of atom (1) A  ii ; B  i ; C  iii (2) A  iv ; B  iii ; C  ii (3) A  i ; B  iv ; C  iii (4) A  ii ; B  iv ; C  iii 13. In an experiment for determination of refractive index of glass of a prism by i -, plot, it was found that a ray incident at angle 35°, suffers a deviation of 40° and that it emerges at angle 79°. In that case which of the following is closest to the maximum possible value of the refractive index ? (1) 1.6 (2) 1.7 (3) 1.8 (4) 1.5 14. A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line? (1) 0.80 mm (2) 0.70 mm (3) 0.50 mm (4) 0.75 mm Part # II 1. The edge of a cube is a = 1.2 × 10–2 m. Then its volume will be recorded as (A) 1.7 × 10–6 m3 2. (B) 1.70 × 10–6 m3 (C) 1.70 × 10–7 m3 (D) 1.78 × 10–6 m3 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 3. [Previous Year Questions][ADVANCED] (B) 2 (C) 3 (D) 4 For the post office box arrangement to determine the value of unknown resistance, the unknown resistance should be connected between B C D A B1 (A) B and C 4. (B) C and D (C) A and D (D) B1 and C1 In a resonance column method, resonance occurs at two successive level of 1 = 30.7 cm and 2= 63.2 cm using a tuning fork of f = 512 Hz. What is the maximum error in measuring speed of sound using relations v = f &  = 2 (2– 1). (A) 256 cm/sec 5. C1 (B) 92 cm/sec (C) 102.4 cm/sec (D) 204.8 cm/sec Graph of position of image vs position of point object from a convex lens is shown. Then, focal length of the lens is v cm 31 30 20 10 u cm 30 31 (A) 0.50 ± 0.05 cm 6. 20 (B) 0.50 ± 0.10 cm 10 0( 9, +9) (C) 5.00 ± 0.05 cm (D) 5.00 ± 0.10 cm  4 2 l  A student performs an experiment for determination of  g  2  ,   1m, and he commits an error of . T   For T he takes the time of n oscillations with the stop watch of least count T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate ? 7. (A) L = 0.5, T = 0.1, n = 20 (B) L = 0.5, T = 0.1, n = 50 (C) L = 0.5, T = 0.01, n = 20 (D) L = 0.1, T = 0.05, n = 50 The circular scale of a screw gauge has 50 divisions and pitch of 0.5 mm. Find the diameter of sphere. Main scale reading is 2 – S N H 0 E 5 K R M (A) 1.2 (B) 1.25 (C) 2.207 (D) 2.25 MEASUREMENT ERROR & EXPERIMENT 8. 9. A student performs an experiment to determine the Young's modulus of a wire, exactly 2m 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/s2 (exact). The Young's modulus obtained from the reading is – (A) (2.0 ± 0.3) × 1011 N/m2 (B) (2.0 ± 0.2) × 1011 N/m2 (C) (2.0 ± 0.1) × 1011 N/m2 (D) (2.0 ± 0.05) × 1011 N/m2 In the experiment to determine the speed of sound using a resonance column – (A) prongs of the tuning fork are kept in a vertical plane. (B) prongs of the tuning fork are kept in a horizontal plane. (C) In one of the two resonance observed, the length of the resonating air column is close to the wavelength of sound in air (D) In one of the two resonance observed, the length of the resonating air column is close to half of the wavelength of sound in air 10. In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student placed the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shift his/her eye towards left, the image appears to the right of the object pin. Then(A) x < f 11. 13. (C) x = 2f (D) x > 2f The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions th equivalent to 2.45 cm. The 24 division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is :(A) 5.112 cm 12. (B) f < x < 2f (B) 5.124 cm (C) 5.136 cm (D) 5.148 cm Using the expression 2d sin  = , one calculates the values of d by measuring the corresponding angles  in the range 0 to 90°. The wavelength  is exactly known and the error in  is constant for all values of . As  increases from 0° :(A) the absolute error in d remains constant (B) the absolute error in d increases (C) the fractional error in d remains constant (D) the fractional error in d decreases There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The vernier scale of one of the calipers (C1) has 10 eaul divisions the correspond to 9 main scale divisions. The vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers a shown in the figure. The measured values (in cm) by calipers C1 and C2, respectively are (A) 2.85 and 2.82 (B) 2.87 and 2.83 (C) 2.87 and 2.86 (D) 2.87 and 2.87 Multiple Choice Questions 1. A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 m. The maximum error in the location of the image can 0.2 m. The 5 sets of (u, v) values recorded by the student (in cm) are : (42, 56), (48, 48),(60, 40), (66, 33), (78, 39). The data set(s) that connot come from experiment and is (are) incorrectly recorded is (are ) (A) (42, 56) (B) (48, 48) (C) (66, 33) (D) (78, 39) 2. A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by resonance and that with the longer air-column is the second resonance. Then, [IIT-JEE 2009] (A) The intensity of the sound heard at the first resonance was more than that at the second resonance (B) the prongs of the tuning fork were kept in a horizontal plane above the resonance tube (C) the amplitude of vibration of the ends of the prongs is typically around 1 cm (D) the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air 3. Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc < R/2, which of the following statement(s) about any one of the galvanometer is(are) true? (A) The maximum voltage range is obtained when all the components are connected in series [IIT-JEE 2016] (B) The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer (C) The maximum current range is obtained when all the components are connected in parallel (D) The maximum current range is obtained when the two galvanometers are connected in series and the combina tion is connected parallel with both the resistors 4. In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true? (A) The voltmeter displays - 5 V as soon as the key is pressed, and displays +5 V after a long time [IIT-JEE 2016] (B) The voltmeter will display 0 V at time t = ln 2 seconds (C) The current in the ammeter becomes 1/e of the initial value after 1 second (D) The current in the ammeter becomes zero after a long time Subjective Questions 1. In a vernier callipers, n divisions of its main scale match with (n + 1) divisions on its vernier scale. Each division of the main scale is a units. Using the vernier principle, calculate its least count. [IIT-JEE 2003] 2. In a Searle's experiment, the diameter of the wire as measured by a screw gauge of least count 0.001 cm is 0.050 cm. The length, measured by a scale of least count 0.1 cm, is 110.0 cm. When a weight of 50N is suspended from the wire, the extension is measured to be 0.125 cm by a micrometer of least count 0.001 cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data. [IIT-JEE 2004] 3. Draw the circuit for experimental verification of Ohm's law using a source of variable D.C. voltage, a main resistance of 100 , two galvanometers and two resistance of values 106  and 10–3  respectively. Clearly show the positions of the voltmeter and the ammeter. [IIT-JEE 2004] 4. The pitch of a screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 mm and 47th division on the circular scale coincides with the reference line. The length of the wire is 5.6 cm. Find the curved surface area (in cm2) of the wire in appropriate number of significant figures. [IIT-JEE 2004] 5. The edge of a cube is measured using a vernier calliper. (9 divisions of the main scale is equal to 10 divisions of vernier scale and 1 main scale division is 1 mm). The main scale division reading is 10 and 1 division of vernier scale was found to be coinciding with the main scale. The mass of the cube is 2.736 g. Calculate the density in g/cm3 upto correct significant figures. [IIT-JEE 2005] ANSWER KEY EXERCISE - 5 : PART # I 1. 3 14. 1 2. 1 3. 4 4. 3 5. 3 6. 2 7. 4 8. 4 9. 2 10. 3 11. 4 12. 1 13. 4 9. A 10. B 11. B 12. D 13. B PART # II Single Choice Questions : 1. A 2. D 3. C 4. D 5. C 6. D 7. A 8. B Multiple Choice Questions 1. C, D 2. A, D Subjective Questions : 4. 2.6 cm2 5. 2.66 g/cm3 3. B,C 1. a n 1 4. A,B,C,D 2.  3.