Errors of Measurement PYQs: JEE Mains Physics

Showing 1–50 of 53 questions

1. 1. Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is : 2026 Medium
2. 2. In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1\) mm. When diameter of a sphere is measured, the reading of main scale is \(5\) mm and \(50^{\text{th}}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm. 2026 Medium
3. 3. In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has 2026 Medium
4. 4. In an experiment the values of two spring constants were measured as \(k _1=(10 \pm 0.2) N / m\)
   and \(k _2=(20 \pm 0.3) N / m\). If these springs are connected in parallel, then the percentage error in equivalent spring constant is : 2026 Easy
5. 5. In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \(10\text{ V}\) and \(5\text{ A}\), respectively. The least counts of voltmeter and ammeter are \(500\text{ mV}\) and \(200\text{ mA}\), respectively. The estimated error in the resistance measurement is _______ \(\Omega\). 2026 Medium
6. 6. The density \(\rho\) of a uniform cylinder is determined by measuring its mass \(m\), length \(l\) and diameter \(d\). The measured values of \(m\), \(l\) and \(d\) are \(97.42 \pm 0.02\) g, \(8.35 \pm 0.05\) mm and \(20.20 \pm 0.02\) mm, respectively. Calculated percentage fractional error in \(\rho\) is _______. 2026 Medium
7. 7. The diameter of a wire measured by a screw gauge of least count \(0.001\) cm is \(0.08\) cm. The length measured by a scale of least count \(0.1\) cm is \(150\) cm. When a weight of \(100\) N is applied to the wire, the extension in length is \(0.5\) cm, measured by a micrometer of least count \(0.001\) cm. The error in the measured Young's modulus is \(\alpha \times 10^9\) N/m\(^2\). The value of \(\alpha\) is _______.
   (Ignore the contribution of the load to Young's modulus error calculation) 2026 Hard
8. 8. The time period of a simple harmonic oscillator is \(T =2 \pi \sqrt{\frac{ k }{ m }}\). The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg , and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant( \(k\) ) is ___________ %. 2026 Medium
9. 9. A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
   The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\). 2025 Easy
10. 10. A physical quantity \(Q\) is related to four observables \(a, b, c, d\) as follows :
    \(\mathrm{Q}=\frac{\mathrm{ab}{ }^4}{\mathrm{~cd}}\)
    
    where, \(\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}\) and \(\mathrm{d}=(50 \pm 0.1) \mathrm{m}\), then the percentage error in Q is \(\frac{x}{1000}\), where \(x=\) ________ . 2025 Medium
11. 11. A quantity Q is formulated as \(\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}\) and Z are independent parameters which have fractional errors of \(0.1,0.2\) and 0.5 , respectively in measurement. The maximum fractional error of Q is _______. 2025 Medium
12. 12. A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \(\frac{x}{100}\) where \(x\) is _________. 2025 Medium
13. 13. The energy of a system is given as \(\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}\), where t is the time and \(\beta=0.3 \mathrm{~s}^{-1}\). The errors in the measurement of \(\alpha\) and \(t\) are \(1.2 \%\) and \(1.6 \%\), respectively. At \(t=5 \mathrm{~s}\), maximum percentage error in the energy is : 2025 Medium
14. 14. The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
    radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
    length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\) 2025 Medium
15. 15. A physical quantity \(Q\) is found to depend on quantities \(a, b, c\) by the relation \(Q=\frac{a^4 b^3}{c^2}\). The percentage error in \(a\), \(b\) and \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(\mathrm{Q}\) is _______. 2024 Hard
16. 16. If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______. 2024 Hard
17. 17. The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______. 2024 Hard
18. 18. The radius ( \(\mathrm{r})\), length \((l)\) and resistance \((\mathrm{R})\) of a metal wire was measured in the laboratory as \(\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}\) \(\mathrm{R}=(100 \pm 10) \mathrm{ohm}\) \(l=(15 \pm 0.2) \mathrm{cm}\) The percentage error in resistivity of the material of the wire is _______. 2024 Hard
19. 19. The resistance \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\) where \(\mathrm{V}=(200 \pm 5) \mathrm{V}\) and \(I=(20 \pm 0.2) A\), the percentage error in the measurement of \(R\) is _______. 2024 Hard
20. 20. A body of mass \((5 \pm 0.5) kg\) is moving with a velocity of \((20 \pm 0.4) m / s\). Its kinetic energy will be 2023 Medium
21. 21. A cylindrical wire of mass \((0.4 \pm 0.01)\,g\) has length \((8 \pm 0.04)\,cm\) and radius \((6 \pm 0.03)\,mm\).The maximum error in its density will be \(......\,\%\) 2023 Medium
22. 22. A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\) 2023 Easy
23. 23. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\) : A spherical body of radius \((5 \pm 0.1)\) \(mm\) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \(4\,\%\). Reason \(R\) : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below on : 2023 Medium
24. 24. Two resistances are given as \(R _1=(10 \pm 0.5)\,\Omega\) and \(R_2=(15 \pm 0.5)\, \Omega\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is 2023 Hard
25. 25. A sliver wire has mass \((0.6 \pm 0.006) \; g\), radius \((0.5 \pm 0.005) \; mm\) and length \((4 \pm 0.04) \; cm\). The maximum percentage error in the measurement of its density will be \(......\,\%\) 2022 Medium
26. 26. A student in the laboratory measures thickness of a wire using screw gauge. The readings are \(1.22\,mm , 1.23\,mm , 1.19\,mm\) and \(1.20\,mm\). The percentage error is \(\frac{ x }{121} \%\). The value of \(x\) is .............. 2022 Medium
27. 27. A torque meter is calibrated to reference standards of mass, length and time each with \(5 \%\) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of\(............\%\) 2022 Medium
28. 28. For \(z=a^{2} x^{3} y^{\frac{1}{2}}\), where \(a\) is a constant. If percentage error in measurement of \(x\) and \(y\) are \(4 \%\) and \(12 \%\), respectively, then the percentage error for \(z\) will be \(%\) 2022 Easy
29. 29. If \(Z=\frac{A^{2} B^{3}}{C^{4}}\), then the relative error in \(Z\) will be 2022 Easy
30. 30. In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\) 2022 Hard
31. 31. In an experiment to find acceleration due to gravity \((g)\) using simple pendulum, time period of \(0.5\,s\) is measured from time of \(100\) oscillation with a watch of \(1\;s\) resolution. If measured value of length is \(10\; cm\) known to \(1\; mm\) accuracy. The accuracy in the determination of \(g\) is found to be \(x \%\). The value of \(x\) is 2022 Medium
32. 32. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are \(1 \%, 2 \%\) and \(3 \%\) respectively. The maximum percentage error in the detection of the dissipated heat will be 2022 Easy
33. 33. A physical quantity \(y\) is represented by the formula \(y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}\). If the percentage error found in \(y, m, r, l\) and \(g\) are \(18,1,0.5,4\) and \(p\) respectively, then find the value of \(x\) and \(p\). 2021 Medium
34. 34. A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.

    Physical Quantity	Least count of the Equipment used for measurement	Observed value
    Mass \(({M})\)	\(1\; {g}\)	\(2\; {kg}\)
    Length of bar \((L)\)	\(1\; {mm}\)	\(1 \;{m}\)
    Breadth of bar \((b)\)	\(0.1\; {mm}\)	\(4\; {cm}\)
    Thickness of bar \((d)\)	\(0.01\; {mm}\)	\(0.4 \;{cm}\)
    Depression \((\delta)\)	\(0.01\; {mm}\)	\(5 \;{mm}\)

    Then the fractional error in the measurement of \({Y}\) is 2021 Hard
35. 35. In order to determine the Young's Modulus of a wire of radius \(0.2\, cm\) (measured using a scale of least count \(=0.001\, cm )\) and length \(1 \,m\) (measured using a scale of least count \(=1\, mm\) ), a weight of mass \(1\, kg\) (measured using a scale of least count \(=1 \,g\) ) was hanged to get the elongation of \(0.5\, cm\) (measured using a scale of least count \(0.001\, cm\) ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in \(\%\)) 2021 Hard
36. 36. The period of oscillation of a simple pendulum is \(T =2 \pi \sqrt{\frac{ L }{ g }} .\) Measured value of \( L \) is \(1.0\, m\) from meter scale having a minimum division of \(1 \,mm\) and time of one complete oscillation is \(1.95\, s\) measured from stopwatch of \(0.01 \,s\) resolution. The percentage error in the determination of \(g\) will be ..... \(\%.\) 2021 Medium
37. 37. The radius of a sphere is measured to be \((7.50 \pm 0.85) \,cm .\) Suppose the percentage error in its volume is \(x\). The value of \(x\), to the nearest integer is .....\(\%\) 2021 Medium
38. 38. The resistance \(R =\frac{ V }{ I },\) where \(V =(50 \pm 2) \;V\) and \(I=(20 \pm 0.2)\;A.\) The percentage error in \(R\) is \(x\%\). The value of \(x\) to the nearest integer is ......... 2021 Medium
39. 39. The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer is ...........\(\%\) 2021 Hard
40. 40. Three students \(S_{1}, S_{2}\) and \(S_{3}\) perform an experiment for determining the acceleration due to gravity \((g)\) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

    Student No.	Length of pendulum \((cm)\)	No. of osci \((n)\)	Total time for osci	Time period \((s)\)
    \(1.\)	\(64.0\)	\(8\)	\(128.0\)	\(16.0\)
    \(2.\)	\(64.0\)	\(4\)	\(64.0\)	\(16.0\)
    \(3.\)	\(20.0\)	\(4\)	\(36.0\)	\(9.0\)

    (Least count of length \(=0.1 \,{m}\), least count for time \(=0.1\, {s}\) ) If \(E_{1}, E_{2}\) and \(E_{3}\) are the percentage errors in \('g'\) for students \(1,2\) and \(3\) respectively, then the minimum percentage error is obtained by student no. ....... . 2021 Hard
41. 41. Two resistors \({R}_{1}=(4 \pm 0.8) \Omega\) and \({R}_{2}=(4 \pm 0.4)\) \(\Omega\) are connected in parallel. The equivalent resistance of their parallel combination will be 2021 Hard
42. 42. A physical quantity \(z\) depends on four observables \(a,\) \(b,\) \(c\) and \(d ,\) as \(z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .\) The percentage of error in the measurement of \(a, b, c\) and \(d\) are \(2 \%, 1.5 \%, 4 \%\) and \(2.5 \%\) respectively. The percentage of error in \(z\) is\(......\%\) 2020 Medium
43. 43. A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\) 2020 Medium
44. 44. The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is \(\left(\frac{x}{100}\right) \% .\) If the relative errors in measuring the mass and the diameter are \(6.0 \%\) and \(1.5 \%\) respectively, the value of \(x\) is 2020 Hard
45. 45. In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\) 2019 Hard
46. 46. In the density measurement of a cube, the mass and edge length are measured as \((10.00 \pm 0.10)\,\,kg\,\) and \((0.10 \pm 0.01)\,\,m\,\) respectively. The error in the measurement of density is 2019 Hard
47. 47. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively \(1.5\%\) and \(1\%\), the maximum error in determining the density is   ........ \(\%\) 2018 Easy
48. 48. The percentage errors in quantities \(P, Q, R\)  and \(S\)  are \(0.5\%,\,1\%,\,3\%\)  and  \(1 .5\%\) respectively in the  measurement of a physical quantity \(A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}\) . the maximum percentage error in the value of \(A\)  will be ........... \(\%\) 2018 Hard
49. 49. The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume is 2018 Hard
50. 50. A physical quantity \(p\) is described by the relation \(p\, = a^{1/2}\, b^2\, c^3\, d^{-4}\) If the relative errors in the measurement of \(a, b, c\) and \(d\) respectively, are \(2\% , 1\%, 3\%\) and \(5\%\), then the relative error in \(P\) will be ........... \(\%\) 2017 Medium

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