Measurement Problems

This section provides 100 problems to test your understanding of measurement, including SI units, dimensional analysis, significant figures, and error analysis. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence.

Numerical Problems

1. Convert a speed of $108km/h$ to $m/s$.

   • (a) $25m/s$
   • (b) $30m/s$
   • (c) $35m/s$
   • (d) $40m/s$

2. A mass of $3.6kg$ experiences an acceleration of $2.45m/s^2$. Calculate the force in newtons with correct significant figures.

   • (a) $8.8N$
   • (b) $8.82N$
   • (c) $9.0N$
   • (d) $9.2N$

3. Convert a length of $1500cm$ to $km$.

   • (a) $0.015km$
   • (b) $0.15km$
   • (c) $1.5km$
   • (d) $15km$

4. A time interval of $7200s$ is equivalent to how many hours?

   • (a) $1h$
   • (b) $2h$
   • (c) $3h$
   • (d) $4h$

5. A velocity of $50m/s$ is equivalent to how many $km/h$?

   • (a) $150km/h$
   • (b) $180km/h$
   • (c) $200km/h$
   • (d) $220km/h$

6. A force of $12.4N$ acts over a distance of $5.62m$. Calculate the work done in joules with correct significant figures.

   • (a) $69J$
   • (b) $69.6J$
   • (c) $70J$
   • (d) $71J$

7. Convert an area of $2500c{m}^2$ to $m^2$.

   • (a) $0.25m^2$
   • (b) $2.5m^2$
   • (c) $25m^2$
   • (d) $250m^2$

8. A power of $500W$ is used for $2.0h$. Calculate the energy in joules with correct significant figures.

   • (a) $3.6\times {10}^{6}J$
   • (b) $3.6\times {10}^{5}J$
   • (c) $1.8\times {10}^{6}J$
   • (d) $1.8\times {10}^{5}J$

9. A length is measured as $8.75m$ with an error of $\pm 0.05m$. Calculate the percentage error.

   • (a) $0.5\mathrm{\%}$
   • (b) $0.57\mathrm{\%}$
   • (c) $0.6\mathrm{\%}$
   • (d) $0.7\mathrm{\%}$

10. Convert a volume of $1.5L$ to $m^3$.

    • (a) $0.0015m^3$
    • (b) $0.015m^3$
    • (c) $0.15m^3$
    • (d) $1.5m^3$

11. A mass of $0.045kg$ is accelerated at $1.23m/s^2$. Calculate the force in newtons with correct significant figures.

    • (a) $0.055N$
    • (b) $0.0554N$
    • (c) $0.056N$
    • (d) $0.06N$

12. Convert a speed of $90km/h$ to $m/s$.

    • (a) $20m/s$
    • (b) $25m/s$
    • (c) $30m/s$
    • (d) $35m/s$

13. A time of $1800s$ is equivalent to how many minutes?

    • (a) $20min$
    • (b) $25min$
    • (c) $30min$
    • (d) $35min$

14. A length of $0.075m$ is equivalent to how many $cm$?

    • (a) $7.5cm$
    • (b) $75cm$
    • (c) $0.75cm$
    • (d) $750cm$

15. A force of $15.6N$ acts over $2.34m$. Calculate the work done in joules with correct significant figures.

    • (a) $36J$
    • (b) $36.5J$
    • (c) $37J$
    • (d) $37.5J$

16. Convert an area of $0.85m^2$ to $c{m}^2$.

    • (a) $850c{m}^2$
    • (b) $8500c{m}^2$
    • (c) $85000c{m}^2$
    • (d) $850000c{m}^2$

17. A power of $200W$ is used for $1.5h$. Calculate the energy in joules with correct significant figures.

    • (a) $1.08\times {10}^{6}J$
    • (b) $1.08\times {10}^{5}J$
    • (c) $5.4\times {10}^{5}J$
    • (d) $5.4\times {10}^{6}J$

18. A length is measured as $6.40m$ with an error of $\pm 0.03m$. Calculate the percentage error.

    • (a) $0.4\mathrm{\%}$
    • (b) $0.47\mathrm{\%}$
    • (c) $0.5\mathrm{\%}$
    • (d) $0.6\mathrm{\%}$

19. Convert a volume of $2500c{m}^3$ to $L$.

    • (a) $2.5L$
    • (b) $25L$
    • (c) $0.25L$
    • (d) $250L$

20. A mass of $1.25kg$ experiences an acceleration of $4.80m/s^2$. Calculate the force in newtons with correct significant figures.

    • (a) $6.0N$
    • (b) $6.00N$
    • (c) $6.1N$
    • (d) $6.2N$

21. Convert a speed of $72km/h$ to $m/s$.

    • (a) $18m/s$
    • (b) $20m/s$
    • (c) $22m/s$
    • (d) $24m/s$

22. A time of $3600s$ is equivalent to how many hours?

    • (a) $0.5h$
    • (b) $1h$
    • (c) $1.5h$
    • (d) $2h$

23. A length of $500mm$ is equivalent to how many $m$?

    • (a) $0.5m$
    • (b) $5m$
    • (c) $50m$
    • (d) $500m$

24. A force of $7.5N$ acts over $1.24m$. Calculate the work done in joules with correct significant figures.

    • (a) $9.3J$
    • (b) $9.30J$
    • (c) $9.5J$
    • (d) $9.8J$

25. Convert an area of $0.045m^2$ to $c{m}^2$.

    • (a) $450c{m}^2$
    • (b) $4500c{m}^2$
    • (c) $45000c{m}^2$
    • (d) $450000c{m}^2$

26. A power of $1000W$ is used for $0.5h$. Calculate the energy in joules with correct significant figures.

    • (a) $1.8\times {10}^{6}J$
    • (b) $1.8\times {10}^{5}J$
    • (c) $9.0\times {10}^{5}J$
    • (d) $9.0\times {10}^{6}J$

27. A length is measured as $3.50m$ with an error of $\pm 0.01m$. Calculate the percentage error.

    • (a) $0.2\mathrm{\%}$
    • (b) $0.29\mathrm{\%}$
    • (c) $0.3\mathrm{\%}$
    • (d) $0.4\mathrm{\%}$

28. Convert a volume of $0.75m^3$ to $L$.

    • (a) $75L$
    • (b) $750L$
    • (c) $7500L$
    • (d) $75000L$

29. A mass of $0.082kg$ is accelerated at $2.15m/s^2$. Calculate the force in newtons with correct significant figures.

    • (a) $0.18N$
    • (b) $0.176N$
    • (c) $0.18N$
    • (d) $0.2N$

30. Convert a speed of $45km/h$ to $m/s$.

    • (a) $10m/s$
    • (b) $12.5m/s$
    • (c) $15m/s$
    • (d) $20m/s$

31. A time of $900s$ is equivalent to how many minutes?

    • (a) $10min$
    • (b) $15min$
    • (c) $20min$
    • (d) $25min$

32. A length of $250cm$ is equivalent to how many $m$?

    • (a) $2.5m$
    • (b) $25m$
    • (c) $0.25m$
    • (d) $250m$

33. A force of $7.5N$ acts over $1.24m$. Calculate the work done in joules with correct significant figures.

    • (a) $9.3J$
    • (b) $9.30J$
    • (c) $9.5J$
    • (d) $9.8J$

34. Convert an area of $0.045m^2$ to $c{m}^2$.

    • (a) $450c{m}^2$
    • (b) $4500c{m}^2$
    • (c) $45000c{m}^2$
    • (d) $450000c{m}^2$

35. A length is measured as $9.80m$ with an error of $\pm 0.02m$. Calculate the percentage error.

    • (a) $0.2\mathrm{\%}$
    • (b) $0.20\mathrm{\%}$
    • (c) $0.3\mathrm{\%}$
    • (d) $0.4\mathrm{\%}$

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Conceptual Problems

36. Which of the following is a base SI unit?

• (a) Newton
• (b) Joule
• (c) Meter
• (d) Watt

37. What is the role of dimensional analysis in physics?

• (a) To measure physical quantities
• (b) To check equation consistency
• (c) To calculate errors
• (d) To convert units

38. How many significant figures are in the number $0.00780$?

• (a) 2
• (b) 3
• (c) 4
• (d) 5

39. What is the primary source of error in a measurement?

• (a) Dimensional inconsistency
• (b) Instrument precision
• (c) Unit conversion
• (d) Significant figures

40. Which unit is derived from base SI units?

• (a) Meter
• (b) Kilogram
• (c) Second
• (d) Newton

41. What does the relative error of a measurement indicate?

• (a) Absolute uncertainty
• (b) Fractional uncertainty
• (c) Percentage uncertainty
• (d) Dimensional consistency

42. How are trailing zeros in a decimal number treated in significant figures?

• (a) Not significant
• (b) Always significant
• (c) Significant only if after a decimal
• (d) Significant only if before a decimal

43. Why is the meter defined using the speed of light?

• (a) To simplify conversions
• (b) To ensure precision
• (c) To match other units
• (d) To reduce errors

44. What happens to significant figures in addition?

• (a) Use the least number of significant figures
• (b) Use the least precise decimal place
• (c) Use the most significant figures
• (d) Use the average significant figures

45. What is the dimension of velocity?

• (a) $[\text{L}{\text{T}}^{-1}]$
• (b) $[\text{L}\text{T}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (d) $[{\text{L}}^2{\text{T}}^{-1}]$

46. How does error propagate in subtraction?

• (a) Subtract absolute errors
• (b) Sum absolute errors
• (c) Multiply relative errors
• (d) Sum percentage errors

47. Which of the following has the same dimensions as energy?

• (a) Force
• (b) Power
• (c) Work
• (d) Velocity

48. What is the purpose of significant figures in measurements?

• (a) To indicate precision
• (b) To convert units
• (c) To check dimensions
• (d) To calculate errors

49. Why are SI units standardized globally?

• (a) To simplify calculations
• (b) To ensure consistency
• (c) To reduce errors
• (d) To match dimensions

50. What is the dimension of pressure?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (c) $[{\text{L}}^{-1}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$

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Derivation Problems

51. Derive the dimensions of power using base SI units.

52. Derive the dimensions of acceleration and express them in terms of base SI units.

53. Derive the dimensions of work using the formula $W=F\cdot d$.

54. Derive the dimensions of pressure using the formula $P=F/A$.

55. Derive the error propagation formula for the sum of two quantities $z=x+y$.

56. Derive the dimensions of velocity using the formula $v=d/t$.

57. Derive the significant figures rule for addition using the concept of precision.

58. Derive the dimensions of force using Newton’s second law.

59. Derive the error propagation formula for the product of two quantities $z=x\cdot y$.

60. Derive the dimensions of energy using the kinetic energy formula $KE=\frac{1}{2}m{v}^2$.

61. Derive the dimensions of area and express them in terms of base SI units.

62. Derive the significant figures rule for multiplication using relative uncertainty.

63. Derive the dimensions of momentum using the formula $p=mv$.

64. Derive the error propagation formula for the difference of two quantities $z=x-y$.

65. Derive the dimensions of density using the formula $\rho =m/V$.

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NEET-style Conceptual Problems

66. Which of the following is a derived SI unit?

• (a) Meter
• (b) Kilogram
• (c) Watt
• (d) Second

67. What is the dimension of time in SI units?

• (a) $[\text{L}]$
• (b) $[\text{M}]$
• (c) $[\text{T}]$
• (d) $[\text{L}{\text{T}}^{-1}]$

68. How many significant figures are in the number $5000.0$?

• (a) 2
• (b) 3
• (c) 4
• (d) 5

69. What does absolute error measure?

• (a) Fractional uncertainty
• (b) Difference between measured and true values
• (c) Percentage uncertainty
• (d) Dimensional consistency

70. Which of the following has the same dimensions as force?

• (a) Work
• (b) Momentum
• (c) Mass times acceleration
• (d) Velocity

71. Why are leading zeros not significant in a number like $0.0023$?

• (a) They indicate precision
• (b) They are placeholders
• (c) They are after a decimal
• (d) They are between non-zeros

72. What is the role of the kelvin in SI units?

• (a) Measures temperature
• (b) Measures length
• (c) Measures mass
• (d) Measures time

73. How does error propagate in addition?

• (a) Sum absolute errors
• (b) Subtract absolute errors
• (c) Multiply relative errors
• (d) Sum percentage errors

74. What is the dimension of work?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (c) $[{\text{L}}^2{\text{T}}^{-2}]$
• (d) $[\text{M}\text{L}{\text{T}}^{-1}]$

75. Why are SI units standardized?

• (a) To simplify calculations
• (b) To ensure consistency
• (c) To reduce errors
• (d) To match dimensions

76. How many significant figures are in the number $123.40$?

• (a) 3
• (b) 4
• (c) 5
• (d) 6

77. What does percentage error indicate?

• (a) Absolute uncertainty
• (b) Fractional uncertainty
• (c) Relative uncertainty in percentage
• (d) Dimensional consistency

78. What is the dimension of velocity?

• (a) $[\text{L}{\text{T}}^{-1}]$
• (b) $[\text{L}\text{T}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (d) $[{\text{L}}^2{\text{T}}^{-1}]$

79. Why are trailing zeros in $0.050$ significant?

• (a) They are placeholders
• (b) They are after a decimal
• (c) They are between non-zeros
• (d) They are not significant

80. Which of the following is a base SI unit?

• (a) Joule
• (b) Watt
• (c) Ampere
• (d) Newton

81. What is the dimension of pressure?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (c) $[{\text{L}}^{-1}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$

82. How does error propagate in multiplication?

• (a) Sum absolute errors
• (b) Subtract absolute errors
• (c) Sum relative errors
• (d) Sum percentage errors

83. What is the role of dimensional analysis in experiments?

• (a) To measure quantities
• (b) To convert units
• (c) To check equation consistency
• (d) To calculate errors

84. How many significant figures are in the number $0.00060$?

• (a) 1
• (b) 2
• (c) 3
• (d) 4

85. What is the dimension of energy?

• (a) $[\text{M}{\text{L}}^2{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (c) $[{\text{L}}^2{\text{T}}^{-2}]$
• (d) $[\text{M}\text{L}{\text{T}}^{-1}]$

86. Why are SI units standardized?

• (a) To simplify calculations
• (b) To ensure consistency
• (c) To reduce errors
• (d) To match dimensions

87. What does relative error measure?

• (a) Absolute uncertainty
• (b) Fractional uncertainty
• (c) Percentage uncertainty
• (d) Dimensional consistency

88. How are leading zeros treated in significant figures?

• (a) Always significant
• (b) Not significant
• (c) Significant only if after a decimal
• (d) Significant only if between non-zeros

89. What is the dimension of acceleration?

• (a) $[\text{L}{\text{T}}^{-2}]$
• (b) $[\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-2}]$
• (d) $[{\text{L}}^2{\text{T}}^{-2}]$

90. How does error propagate in addition?

• (a) Sum absolute errors
• (b) Subtract absolute errors
• (c) Multiply relative errors
• (d) Sum percentage errors

91. What is the role of the ampere in SI units?

• (a) Measures current
• (b) Measures length
• (c) Measures mass
• (d) Measures time

92. How many significant figures are in the number $1200$?

• (a) 2
• (b) 3
• (c) 4
• (d) 5

93. What does absolute error indicate?

• (a) Fractional uncertainty
• (b) Difference between measured and true values
• (c) Percentage uncertainty
• (d) Dimensional consistency

94. What is the dimension of density?

• (a) $[\text{M}{\text{L}}^{-3}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-3}]$
• (c) $[{\text{L}}^{-3}]$
• (d) $[\text{M}{\text{L}}^3]$

95. Why are trailing zeros in $0.0700$ significant?

• (a) They are placeholders
• (b) They are after a decimal
• (c) They are between non-zeros
• (d) They are not significant

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NEET-style Numerical Problems

96. A length is measured as $5.60m$ with an error of $\pm 0.04m$. What is the percentage error?

• (a) $0.7\mathrm{\%}$
• (b) $0.71\mathrm{\%}$
• (c) $0.8\mathrm{\%}$
• (d) $0.9\mathrm{\%}$

97. Convert a speed of $36km/h$ to $m/s$.

• (a) $8m/s$
• (b) $10m/s$
• (c) $12m/s$
• (d) $14m/s$

98. A mass of $0.065kg$ is accelerated at $3.20m/s^2$. What is the force in newtons with correct significant figures?

• (a) $0.21N$
• (b) $0.208N$
• (c) $0.22N$
• (d) $0.23N$

99. Convert a volume of $1.8m^3$ to $L$.

• (a) $180L$
• (b) $1800L$
• (c) $18000L$
• (d) $180000L$

100. A force of $6.4N$ acts over $2.50m$. What is the work done in joules with correct significant figures?
     - (a) $16J$
     - (b) $16.0J$
     - (c) $16.5J$
     - (d) $17J$

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