Unit dimension and error questions with solutions

Showing 1–10 of 300 questions

• MatchmediumUnit dimension and errorsignificant number

  Match each operation or situation in List 1 with the correct reporting rule in List 2 and choose the correct option.

  List 1

  1. Addition of measured quantities

  2. Multiplication of measured quantities

  3. Exact counted number

  4. Writing 200 with exactly 3 significant figures

  List 2

  1. Infinite significant figures

  2. Use least number of decimal places

  3. 2.00 × 10²

  4. Use least number of significant figures

  Options

  • Option A

    P-2, Q-4, R-1, S-3

  • Option B

    P-4, Q-2, R-1, S-3

  • Option C

    P-2, Q-1, R-4, S-3

  • Option D

    P-3, Q-4, R-1, S-2

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• MCQeasyUnit dimension and errorunit and conversion of units

  A pressure of 2×10⁵ Pa is expressed in a system where M′=10 kg, L′=2 m and T′=5 s. Its numerical value is:

  Options

  • Option A

    2×10⁴

  • Option B

    4×10⁴

  • Option C

    1×10⁶

  • Option D

    5×10⁵

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• MCQdifficultUnit dimension and errorvernier callipers and screw gauge

  A stack of 25 identical metal sheets is measured by a screw gauge. The observed total thickness is 8.46 mm and the zero error is +0.06 mm. Assuming negligible compression, the thickness of one sheet is:

  Options

  • Option A

    0.324 mm

  • Option B

    0.336 mm

  • Option C

    0.348 mm

  • Option D

    0.360 mm

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• MCQeasyUnit dimension and errorunit and conversion of units

  In a new system, unit mass = 4 kg, unit length = 2 m and unit time = 5 s. A force of 100 N has numerical value:

  Options

  • Option A

    31.25

  • Option B

    312.5

  • Option C

    125

  • Option D

    25

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• MCQmediumUnit dimension and errorvernier callipers and screw gauge

  The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

  Options

  • Option A

    2.5 g/cm³

  • Option B

    1.7 g/cm³

  • Option C

    2.2 g/cm³

  • Option D

    2.0 g/cm³

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• MCQeasyUnit dimension and errorError and its addition ,subtraction,multipication and division

  If y = A²B³/C¹ᐟ² and maximum percentage errors in A, B and C are 1%, 2% and 4%, respectively, maximum percentage error in y is:

  Options

  • Option A

    6%

  • Option B

    8%

  • Option C

    10%

  • Option D

    12%

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• Multi-correctdifficultUnit dimension and errorvernier callipers and screw gauge

  A cylindrical wire is measured using a screw gauge. Its corrected diameter is d and length is L. Which statements are correct?

  Select all that apply

  • Option A

    Cross-sectional area is πd²/4.

  • Option B

    For fixed resistivity and length, resistance varies as 1/d².

  • Option C

    A 1% error in diameter produces approximately 2% error in calculated area.

  • Option D

    A 1% error in diameter produces approximately 1% error in calculated resistance.

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• MCQeasyUnit dimension and errorunit and conversion of units

  If mass unit is doubled, length unit tripled and time unit unchanged, the numerical value of a given force becomes:

  Options

  • Option A

    6 times old

  • Option B

    1/6 of old

  • Option C

    2/3 of old

  • Option D

    3/2 of old

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• MCQeasyUnit dimension and errorDimension and its application

  Match List-I with List-II.

  List-I
  A. Coefficient of viscosity
  B. Surface Tension
  C. Angular momentum
  D. Rotational kinetic energy

  List-II I. [ML²T⁻²] II. [ML²T⁻¹] III. [ML⁻¹T⁻¹] IV. [ML⁰T⁻²]

  Options

  • Option A

    A–II, B–I, C–IV, D–III

  • Option B

    A–I, B–II, C–III, D–IV

  • Option C

    A–III, B–IV, C–II, D–I

  • Option D

    A–IV, B–III, C–II, D–I

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  JEE Mains 2024 30 Jan Morning Shift

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• MatchdifficultUnit dimension and errorvernier callipers and screw gauge

  Match each instrument specification in List I with the correct least count in List II.

  List 1

  1. 50 VSD = 48 MSD; 1 MSD = 0.5 mm

  2. 100 VSD = 97 MSD; 1 MSD = 1 mm

  3. Screw gauge: pitch = 0.4 mm, circular divisions = 80

  4. 25 VSD = 24 MSD; 1 MSD = 1 mm

  List 2

  1. 0.005 mm

  2. 0.020 mm

  3. 0.030 mm

  4. 0.040 mm

  Options

  • Option A

    P-2, Q-3, R-1, S-4

  • Option B

    P-3, Q-2, R-4, S-1

  • Option C

    P-2, Q-4, R-1, S-3

  • Option D

    P-1, Q-3, R-2, S-4

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