Free NEET Physics multiple-choice questions on Errors in Measurement. Attempt each question and reveal the answer with a full explanation.
A screw gauge has a least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is: 0.5 mm 0.25 mm 0.01 mm 1.0 mm The percentage error in the measurement of the density of a cube is computed by measuring its mass and side. If the error in mass is 1 % and the error in side is 1 % , the error in density is: 4% 2% 3% 1% A rectangular plate has length L = (10.0 0.1) cm and width W = (5.0 0.1) cm. The maximum absolute error in the calculated area is: 1.5 cm 2 0.01 cm 2 0.5 cm 2 0.2 cm 2 A student measures the time period of 100 oscillations of a simple pendulum as 90 s, 91 s, 95 s and 92 s. The least count of the watch is 1 s. The value of the time period should be reported as: (92 ± 2) s (92 ± 1.5) s (92 ± 5) s (92 ± 3) s A student measures the thickness of a wire using a screw gauge. The main scale reading is 1 mm and the circular scale reading is 47 divisions. If the screw gauge has 50 divisions on the circular scale and a pitch of 0.5 mm, the thickness is: 1.47 mm 1.94 mm 1.047 mm 1.235 mm In the measurement of the density of a solid sphere, the percentage errors in mass and diameter are 2.4 % and 1.2 % respectively. The maximum error in the density will be: 6.0 % 3.6 % 4.8 % 3.2 % The significant figures in the sum of 12.5 and 0.125 is: 3 4 5 2 A student measures the length of a rod as L = 10.0 cm and width W = 1.00 cm. The area should be reported as: 10.0 cm 2 10 cm 2 10.00 cm 2 10.000 cm 2 A thin wire has a length of (20.0 ± 0.1) cm and a radius of (0.50 ± 0.01) cm. The maximum percentage error in the volume of the wire is: 4.5 % 2.5 % 3.5 % 5.5 % The number of significant figures in the result of the calculation 12.5 - 1.25 is: 3 2 4 5 In a measurement, a value is given as 0.0000700 m. The number of significant figures is: 3 1 2 7 Rounding off the number 12.350 to three significant figures gives: 12.4 12.3 12.40 12.0 If the percentage error in the measurement of the length of a side of a cube is 1.5 % , then the percentage error in the measurement of its volume will be: 4.5 % 3.0 % 1.5 % 2.25 % A physical quantity x is measured as x = (2.00 0.01) cm. The relative error in x 2 is: 0.01 0.005 0.02 0.1 If the error in the measurement of the radius of a cylinder is 2 % and that in its height is 5 % , the maximum error in its volume will be: 9 % 7 % 12 % 10 % The main scale of a vernier calipers has n divisions per cm. n divisions of the vernier scale coincide with (n-1) divisions of main scale. The least count of the vernier calipers is: 1/n 2 cm 1/n cm 1/(n(n+1)) cm 1/(n-1) cm The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm respectively. The area of the sheet in appropriate significant figures and error is: 164 3 cm 2 163.62 2.6 cm 2 163.6 2.6 cm 2 164 2.6 cm 2 A student measures the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is: 0.529 cm 0.521 cm 0.053 cm 0.525 cm Value of 5.335 and 5.345 rounded off to three significant figures are respectively: 5.34, 5.34 5.33, 5.34 5.34, 5.35 5.33, 5.35 A physical quantity P is related to four observables a, b, c and d as P = a 3 b 2 / ( c d) . The percentage errors in a, b, c and d are 1 %, 3 %, 4 % and 2 % respectively. The percentage error in P is: 13 % 10 % 7 % 4 % A screw gauge has a pitch of 1 mm and 100 divisions on its circular scale. When nothing is put in between the studs, the zero of the circular scale lies 4 divisions below the reference line. When a wire is placed, the main scale reads 2 mm and the circular scale reads 42 divisions. The diameter of the wire is: 2.38 mm 2.46 mm 2.42 mm 2.50 mm A student measures the distance x as (10.0 0.1) m and time t as (2.0 0.1) s. The velocity v = x/t should be reported as: (5.0 0.3) m/s (5.00 0.05) m/s (5.0 0.1) m/s (5 0.2) m/s In the measurement of the focal length of a concave mirror, the values of u and v are (20.0 0.1) cm and (20.0 0.1) cm. The maximum error in the focal length f is: 0.1 cm 0.2 cm 0.05 cm 0.4 cm The number of significant figures in the measured value 0.000450 is: 3 4 6 7 The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box up to correct significant figures is: 2.3 kg 2.34 kg 2.340 kg 2.34032 kg A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 92 s, and 95 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be: 92 2 s 92 5 s 92 1.8 s 92 3 s The value of (3.5 0.1) (2.0 0.2) in correct significant figures and error is: 7.0 0.9 7.0 0.3 7 1 7.00 0.90 A student measures the time period of a simple pendulum. The readings are 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. The mean absolute error is: 0.11 s 0.10 s 0.12 s 0.01 s Two resistors R 1 = (20 Ω ± 0.2 Ω ) and R 2 = (40 Ω ± 0.4 Ω ) are connected in parallel. The equivalent resistance R p and the maximum percentage error in it are approximately: 13.3 Ω and 1.00 % 13.3 Ω and 1.5 % 60.0 Ω and 1.00 % 13.3 Ω and 3.00 % If the percentage error in the measurement of the momentum of a particle is 50 % , then the percentage error in its kinetic energy will be: 125 % 100 % 75 % 50 % The significant figures in 1.00 10 3 and 1000 are respectively: 3 and ambiguous (often taken as 1) 3 and 4 1 and 1 3 and 3 How many significant figures are there in 0.003040 and 3.040 10 -3 respectively? 4 and 4 6 and 4 3 and 3 4 and 7 A screw gauge has a pitch of 1.0 mm and 200 divisions on its circular scale. The least count of the screw gauge is: 0.005 mm 0.01 mm 0.02 mm 0.05 mm If the error in measurement of the radius of a sphere is 3 % , then the percentage error in the measurement of its volume is: 9 % 3 % 6 % 1 % How many significant figures are present in the number 0.002030 ? 4 2 3 6 A physical quantity X = M a L b T c . The maximum percentage error in X is given by: (a M M + b L L + c T T ) 100 (a+b+c) 100 ( M M + L L + T T ) 100 (a 2 M M + b 2 L L + c 2 T T ) 100 The number of significant figures in the measurement 1.0007 is: 5 1 4 2 Planck's constant h has a value of 6.626 10 -34 J s . The number of significant figures in this value is: 4 3 7 Infinite The number of significant figures in 0.000070 is: 2 1 6 7 Compare the precision of two measurements: x = 2.50 cm and y = 2.500 cm. Which of the following statements is true? y is more precise than x x is more precise than y Both are equally precise Precision cannot be determined from the values A physical quantity P depends on mass m and height h as P = mgh . If the percentage error in m is 1 % and in h is 1.5 % , and g is assumed to be constant, the percentage error in P is: 2.5 % 0.5 % 1.5 % 3.0 % The percentage error in the measurement of power P = VI . If the percentage error in voltage V is 3 % and in current I is 2 % , the maximum percentage error in power is: 5 % 1 % 6 % 1.5 % A screw gauge has a pitch of 1.0 mm and 100 divisions on its circular scale. The least count of the instrument is: 0.01 mm 0.1 mm 0.001 mm 1.0 mm The error in the measurement of the radius of a sphere is 0.5 % . The percentage error in the measurement of its volume is: 1.5 % 0.5 % 1.0 % 3.0 % If the error in the measurement of the radius of a sphere is a , then the error in the measurement of its surface area is: 2a 3a a/2 4a The error in the calculation of the area of a circle is 4 % . What is the error in the measurement of its radius? 2 % 4 % 8 % 1 % The numbers 6.735 and 6.725 are rounded off to two decimal places. The results are: 6.74 and 6.72 6.73 and 6.73 6.74 and 6.73 6.73 and 6.72 The number of significant figures in Avogadro's number 6.022 10 23 mol -1 is: 4 23 3 infinite If the error in the measurement of the diameter of a sphere is 1 % , then the error in the measurement of its volume is: 3 % 1 % 1.5 % 6 % In a measurement, the value is recorded as 2.00 mm. If the least count of the instrument is 0.01 mm, the percentage error is: 0.5 % 0.01 % 0.005 % 1.0 % A student measures the length of a rod as L = (10.0 0.1) cm. The percentage error in the measurement is: 1.0 % 0.1 % 10 % 0.01 % In the calculation of Z = A 4 B 1/3 / C D 3/2 , the relative error in Z is given by: 4 A A + 1 3 B B + C C + 3 2 D D 4 A A + 1 3 B B - C C - 3 2 D D 4 A A + 1 3 B B + C C - 3 2 D D A 4A + 3 B B + C C + 2 D 3D The error in the measurement of the radius of a sphere is 1 % . The error in the measurement of its surface area will be: 2 % 1 % 3 % 4 % If the error in the measurement of the radius of a sphere is 1 % , then the error in the measurement of its volume will be: 3 % 1 % 1 3 % 0.5 % The error in the measurement of the side of a cube is 2 % . The error in the measurement of its surface area is: 4 % 2 % 6 % 8 % If the error in the measurement of radius of a sphere is 2 % , then the error in the determination of volume of the sphere will be: 6 % 4 % 2 % 8 % The value of 1.20 10 3 has how many significant figures? 3 2 5 4 In a vernier calipers, 10 divisions of vernier scale coincide with 9 divisions of the main scale (in which 1 division is 1 mm). The least count of the instrument is: 0.1 mm 0.01 mm 0.9 mm 0.09 mm The number of significant figures in 0.00010 is: 2 1 5 4 If the error in measurement of the radius of a circle is 1.5 % , then the maximum percentage error in the measurement of its area is: 3.0% 1.5% 2.25% 4.5% A physical quantity Y = a 2b 3/c 4 . The relative error in Y is: 2 a a + 3 b b + 4 c c 2 a a + 3 b b - 4 c c ( a a ) 2 + ( b b ) 3 + ( c c ) 4 a a + b b + c c The percentage error in the measurement of the curved surface area of a cylinder is calculated by measuring its radius r and height h . If the errors in r and h are 1 % and 2 % respectively, the maximum error in the curved surface area is: 3 % 4 % 1 % 5 % The value of 2.5 10 4 has how many significant figures? 2 1 5 4 A physical quantity X is calculated from X = ab 2/c 3 . If percentage errors in a, b, c are 2 %, 1 %, 3 % , the percentage error in X is: 13 % 7 % 12 % 6 % The value of 0.0528 rounded off to two significant figures is: 0.053 0.052 0.05 0.53 A physical quantity P is given by P = A 2 B / C . The percentage errors in the measurement of A, B and C are 1 %, 2 % and 3 % respectively. The maximum percentage error in P is: 7 % 6 % 4 % 10 % If the error in the measurement of the radius of a circle is 1.5 % , what is the percentage error in the measurement of its area? 3.0 % 1.5 % 2.25 % 0.75 % Two resistors R 1 = (100 3) and R 2 = (200 4) are connected in series. The equivalent resistance is: (300 7) (300 1) (300 12) (300 3.5) A screw gauge gives the following readings 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 on the circular scale. The diameter of the wire from the above data is: 0.052 cm 0.52 cm 0.026 cm 0.005 cm In an experiment, four quantities a, b, c and d are measured with percentage error 1 % , 2 % , 3 % and 4 % respectively. Quantity P is calculated as P = a 3b 2 cd .% error in P is: 14 % 10 % 7 % 4 % A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g , the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e 1 and e 2 respectively, the percentage error in the estimation of g is: e 1 + 2e 2 e 1 + e 2 e 1 - 2e 2 e 2 - 2e 1 In the measurement of the volume of a sphere, the error in the determination of the diameter is 3 % . The percentage error in the determination of the surface area of the sphere will be: 6% 9% 12% 3% The percentage errors in the measurement of mass and speed are 2 % and 3 % respectively. The error in kinetic energy obtained by measuring mass and speed will be: 8 % 2 % 12 % 10 % Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m? 9.98 m 9.980 m 9.9 m 9.9801 m A physical quantity X is given by X = 2k 3l 2 m n . The percentage errors in the measurements of k, l, m and n are 1 %, 2 %, 3 % and 4 % respectively. The value of percentage error in X is: 12 % 8 % 10 % 16 % If the capacitance of a nanocapacitor is measured as C = (2.0 0.1) F and the potential difference is V = (10 0.5) V , the percentage error in the stored energy U = 1 2 CV 2 is: 15 % 10 % 5 % 20 % The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are 3 % and 2 % respectively, the maximum error in the measurement of density is: 9 % 7 % 5 % 1 % The value of 2.345 and 2.335 rounded off to three significant figures are respectively: 2.34 and 2.34 2.35 and 2.33 2.35 and 2.34 2.34 and 2.33 In an experiment, the percentage errors that occur in the measurement of physical quantities A, B, C and D are 1 %, 2 %, 3 % and 4 % respectively. Then the maximum percentage error in the measurement of X , where X = A 2 B 1/2 C 1/3 D 3 , is: 16 % 10 % -10 % 12 % A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier calipers, the least count is: 0.2 mm 0.1 mm 0.02 mm 0.05 mm The percentage error in the measurement of the length of a simple pendulum is 1 % and the error in the period is 2 % . The maximum error in the measurement of acceleration due to gravity g is: 5 % 4 % 3 % 1 % A student performs an experiment to determine the Young's modulus of a wire. He finds that Y = MgL r 2 l . If the maximum percentage error in M, L, r and l are a, b, c and d respectively, then the maximum percentage error in Y is: a + b + 2c + d a + b + c + d a + b - 2c - d a + b + c 2 + d The number of significant figures in the measurement 0.04050 is: 4 3 5 2 The sum of the numbers 436.32 , 227.2 and 0.301 in appropriate significant figures is: 663.8 663.821 664 663.82 A force F is applied on a square plate of side L . If the percentage error in the determination of L is 2 % and that in F is 4 % , what is the permissible error in pressure? 8 % 6 % 4 % 2 % A student measures the length of a rod as 2.50 cm, 2.52 cm and 2.48 cm. The average absolute error is: 0.013 cm 0.02 cm 0.01 cm 0.1 cm If the error in the measurement of the radius of a cylinder is 2 % and the error in its height is 3 % , the maximum percentage error in the measurement of its volume is: 7 % 5 % 8 % 1 % The measurement of a physical quantity X depends on a and b as X = a - b . If the absolute errors in a and b are a and b , the absolute error in X is: a + b a - b a b a + b 2 The significant figures in 500.0 are: 4 3 1 2 A student measures the thickness of a human hair by looking at it through a microscope of magnification 100 . He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. The estimated thickness of hair is: 0.035 mm 3.5 mm 0.35 mm 0.0035 mm The mass of a body is 2.000 g and its volume is 1.0 cm 3 . The density of the body up to correct significant figures is: 2.0 g/cm 3 2.00 g/cm 3 2.000 g/cm 3 2 g/cm 3 In an experiment, the voltage across a resistor is measured as V = (100 5) V and the current is I = (10 0.2) A. The percentage error in the resistance R is: 7 % 5 % 2 % 10 % The percentage errors in the measurement of mass and radius of a solid sphere are 2 % and 1 % respectively. The maximum percentage error in the measurement of its density is: 5 % 3 % 4 % 6 % The error in the measurement of the period of a simple pendulum is 2 % and the error in the measurement of its length is 1 % . The percentage error in the measurement of g is: 5% 3% 4% 1% A screw gauge has 50 divisions on its circular scale and a pitch of 0.5 mm. When measuring a diameter, the main scale reading is 2.5 mm and the 20 th circular scale division coincides with the reference line. The measured diameter is: 2.70 mm 2.52 mm 2.60 mm 2.80 mm In a vernier calipers, 20 divisions of the vernier scale coincide with 19 divisions of the main scale. If each main scale division is 0.5 mm, the least count of the instrument is: 0.025 mm 0.01 mm 0.05 mm 0.005 mm If the percentage error in the measurement of the temperature of a hot body is 1 % , then the percentage error in the measurement of the total radiant energy emitted by it (according to Stefan's Law) will be: 4 % 1 % 2 % 0.5 % The value of 2.745 and 2.735 rounded off to three significant figures are respectively: 2.74 and 2.74 2.75 and 2.74 2.74 and 2.73 2.75 and 2.73 A student measures the value of g = 4 2 L T 2 . The errors in measurement of L and T are L and T respectively. The maximum percentage error in g is: ( L L + 2 T T ) 100 ( L L + T T ) 100 ( L L - 2 T T ) 100 ( L L + 1 2 T T ) 100 Rounding off 15.753 to one decimal place gives: 15.8 15.7 15.75 16.0 In a vernier calipers, 10 divisions of the vernier scale coincide with 11 divisions of the main scale. If each main scale division is 1 mm, the least count of the instrument is: 0.1 mm 1.1 mm 0.01 mm 1.0 mm If the error in the measurement of the momentum of a particle is 20 % , then the error in its kinetic energy will be: 44 % 40 % 20 % 10 % The area of a square is 5.29 cm 2 . The side of the square should be expressed as (keeping significant figures in mind): 2.30 cm 2.3 cm 2.300 cm 2.29 cm The length of a simple pendulum is 100 cm known to 1 mm accuracy. The time for 100 oscillations is 200 s measured with a watch of 1 s resolution. The percentage error in the measurement of g is: 1.1 % 2.1 % 0.5 % 1.5 % A student measures the thickness of a wire using a screw gauge. The zero of the circular scale is 3 divisions below the reference line when the studs are in contact. This is called: Positive zero error Negative zero error Parallax error Least count error The value of 10.0 cm + 0.01 cm rounded off to correct significant figures is: 10.0 cm 10.01 cm 10 cm 10.010 cm The value of (1.20 0.01) m (10.0 0.1) m should be reported as: (12.0 0.2) m 2 (12.0 0.1) m 2 (12.00 0.22) m 2 (12.0 0.01) m 2 Which of the following is the most precise measurement? 5.00 mm 5.0 mm 5 mm 0.005 m The resistivity of a wire is given by = r 2 R l . If the percentage errors in the measurement of radius r , resistance R , and length l are 2 % , 1 % , and 1.5 % respectively, the maximum percentage error in the resistivity is: 6.5% 4.5% 3.5% 2.5% A screw gauge with a pitch of 0.5 mm and 100 divisions on the circular scale is used to measure the thickness of a sheet. If the main scale reading is 2 mm and the 45 th division of the circular scale coincides with the reference line, the thickness of the sheet is: 2.225 mm 2.450 mm 2.045 mm 2.500 mm In a Vernier caliper, 50 divisions of the Vernier scale coincide with 49 divisions of the main scale. If each main scale division is 0.5 mm, the least count of the caliper is: 0.01 mm 0.02 mm 0.05 mm 0.1 mm The value of the product 1.2 1.20 should be expressed as: 1.4 1.44 1.440 1.5 Rounding off the number 4.445 to two decimal places gives: 4.44 4.45 4.46 4.40 A force F is applied to a wire of radius r and length L . The stress in the wire is F/( r 2) . If the percentage error in F is 1 % , in r is 2 % , and in L is 1 % , the percentage error in the stress is: 5% 4% 3% 2% When 2.645 and 2.635 are rounded off to two decimal places, we get: 2.64 and 2.64 2.65 and 2.63 2.64 and 2.63 2.65 and 2.64 Which of the following measurements is most precise? 5.000 mm 5.00 mm 5.0 mm 5 cm A physical quantity P is given by P = A 2 B 1/2 C . If the percentage errors in the measurement of A, B, and C are 2 %, 4 %, and 3 % respectively, then the maximum percentage error in P is: 9 % 10 % 7 % 12 % A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 18 main scale divisions. The least count of the vernier calipers is: 0.1 mm 0.02 mm 0.05 mm 0.2 mm The length of a cylinder is measured as 10.0 cm with a meter scale of least count 0.1 cm. The radius is measured as 2.00 cm with a vernier caliper of least count 0.01 cm. The maximum percentage error in the calculated volume of the cylinder is: 2 % 1 % 3 % 4 % A physical quantity P is given by P = a 3 b 2 c d . The percentage errors in a, b, c and d are 1 % , 3 % , 4 % and 2 % respectively. The maximum percentage error in P is: 13 % 7 % 12 % 10 % The density of a wire is measured by measuring its mass and diameter. If the error in mass is 1 % and in diameter is 2 % , the error in density is: 5 % 3 % 4 % 6 % The value of 2.5 + 2.34 + 1.234 up to correct significant figures is: 6.1 6.074 6.07 6.0 If the length of a rod is (10.0 0.1) cm and its breadth is (5.0 0.1) cm, the percentage error in its area is: 3 % 1 % 2 % 4 % A student measures the acceleration due to gravity g using a simple pendulum. The length of the pendulum is L = (100 0.1) cm and the time period is T = (2.00 0.01) s. The maximum percentage error in the measurement of g is: 1.1 % 0.6 % 2.1 % 3.0 % The number of significant figures in 0.0001020 is: 4 7 3 5 A body is dropped from a height. If the error in the measurement of time of fall is 2 % , the percentage error in the calculation of the height (assuming g is constant) is: 4 % 2 % 1 % 0.5 %