Units, Dimensions, Measurements and Errors questions with solutions

Showing 1–10 of 447 questions

• MCQmediumUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  If the dimensional formula of a physical quantity is [MᵃLᵇTᶜ], then the physical quantity will be:

  Options

  • Option A

    pressure, if a=1, b=-1, c=-2

  • Option B

    velocity, if a=1, b=0, c=-1

  • Option C

    acceleration, if a=1, b=1, c=-2

  • Option D

    force, if a=0, b=-1, c=-2

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  AIPMT Screening 2009NEET

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• MCQmediumUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  If the numerical value of a physical quantity is n in a system whose fundamental units are M, L, T, and the units are changed to M′=αM, L′=βL, T′=γT, then for [Q]=[MᵃLᵇTᶜ], n′ equals:

  Options

  • Option A

    n α⁻ᵃβ⁻ᵇγ⁻ᶜ

  • Option B

    n αᵃβᵇγᶜ

  • Option C

    n/(α+β+γ)

  • Option D

    n αᵃ⁺ᵇ⁺ᶜ

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• IntegereasyUnits, Dimensions, Measurements and ErrorsSignificant Figures and Rules of Rounding Off

  Enter the number of significant figures in 0.000700.

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• MCQeasyUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  The dimensional formula of angular impulse is:

  Options

  • Option A

    [ML⁻²T⁻¹]

  • Option B

    [ML²T⁻²]

  • Option C

    [MLT⁻¹]

  • Option D

    [ML²T⁻¹]

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• MCQeasyUnits, Dimensions, Measurements and ErrorsSignificant Figures and Rules of Rounding Off

  The number 2.300 × 10⁵ contains how many significant figures?

  Options

  • Option A

    2

  • Option B

    3

  • Option C

    4

  • Option D

    5

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• MCQdifficultUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference, σ the electrical conductivity and κ the thermal conductivity. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, find the dimensional formula of Z = S²σ/κ.

  Options

  • Option A

    [M⁰L⁰T⁰I⁰K⁰]

  • Option B

    [M⁰L⁰T⁰I⁰K⁻¹]

  • Option C

    [M¹L²T⁻²I⁻¹K⁻¹]

  • Option D

    [M¹L²T⁻⁴I⁻¹K⁻¹]

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  JEE Advanced 2025 Paper 2

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• MCQeasyUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  A physical quantity has dimensions [M⁻¹L³T⁻²]. If mass, length and time units become 2, 3 and 1/2 times old units, its new numerical value is:

  Options

  • Option A

    54 times old

  • Option B

    1/54 of old

  • Option C

    27/8 of old

  • Option D

    8/27 of old

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• MCQeasyUnits, Dimensions, Measurements and ErrorsDimensional Analysis and Its Applications

  Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

  Options

  • Option A

    T² = 4π²r²/(GM)

  • Option B

    T² = 4π²r³

  • Option C

    T² = 4π²r³/(GM)

  • Option D

    T² = 4π²r²/(GM)

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• MCQdifficultUnits, Dimensions, Measurements and ErrorsErrors in Measurement and Error Propagation

  Two resistors R₁ = (20 ± 1) Ω and R₂ = (30 ± 3) Ω are connected in parallel. The maximum percentage error in their equivalent resistance is:

  Options

  • Option A

    5%

  • Option B

    7%

  • Option C

    8%

  • Option D

    15%

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• MCQmediumUnits, Dimensions, Measurements and ErrorsErrors in Measurement and Error Propagation

  The time period of a simple harmonic oscillator is

  T = 2π√(m/k).

  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 _______ %.

  Options

  • Option A

    3.43

  • Option B

    3.35

  • Option C

    7.60

  • Option D

    6.76

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