Dimension and its application questions with solutions

Showing 1–10 of 118 questions

• MCQmediumUnit dimension and errorDimension and its application

  (P + a/V²)(V - b) = RT represents an equation of state. P is pressure, V is volume, T is temperature and a, b, R are constants. The physical quantity having the same dimensional formula as b²/a is:

  Options

  • Option A

    Bulk modulus

  • Option B

    Modulus of rigidity

  • Option C

    Compressibility

  • Option D

    Energy density

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  JEE Mains1 February 2023Shift 1Morning Shift

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• MCQmediumUnit dimension and errorDimension and its application

  The dimensions [M L T⁻² A⁻²] belong to:

  Options

  • Option A

    self inductance

  • Option B

    magnetic permeability

  • Option C

    electric permittivity

  • Option D

    magnetic flux

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• MCQeasyUnit dimension and errorDimension and its application

  If energy E, length L and time T are taken as fundamental units, dimensions of mass are:

  Options

  • Option A

    [ET²L⁻²]

  • Option B

    [EL⁻²T⁻²]

  • Option C

    [E⁻¹L²T⁻²]

  • Option D

    [ET⁻²L²]

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• MCQmediumUnit dimension and errorDimension and its application

  What is the dimensional formula of ab⁻¹ in the equation (P + a/V²)(V - b) = RT, where letters have their usual meaning.

  Options

  • Option A

    [M⁰L³T⁻²]

  • Option B

    [ML²T⁻²]

  • Option C

    [M⁻¹L⁵T³]

  • Option D

    [M⁶L⁷T⁴]

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  JEE Mains 2024 05 Apr Evening Shift

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• MCQmediumUnit dimension and errorDimension and its application

  Given below are two statements :

  Statement (I) : Dimensions of specific heat is [L²T⁻²K⁻¹]

  Statement (II) : Dimensions of gas constant is [ML²T⁻¹K⁻¹]

  Choose the correct answer from the options given below :

  Options

  • Option A

    Statement (I) is incorrect but statement (II) is correct

  • Option B

    Both statement (I) and statement (II) are incorrect

  • Option C

    Statement (I) is correct but statement (II) is incorrect

  • Option D

    Both statement (I) and statement (II) are correct

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  JEE Mains 2024 06 Apr Evening Shift

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• MCQeasyUnit dimension and errorDimension and its application

  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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• MatchmediumUnit dimension and errorDimension and its application

  Match List-I with List-II.

  List 1

  1. (a) Gravitational constant G

  2. (b) Gravitational potential energy

  3. (c) Gravitational potential

  4. (d) Gravitational intensity

  List 2

  1. (i) [L² T⁻²]

  2. (ii) [M⁻¹ L³ T⁻²]

  3. (iii) [L T⁻²]

  4. (iv) [M L² T⁻²]

  Options

  • Option A

    (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

  • Option B

    (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

  • Option C

    (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

  • Option D

    (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

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• MCQeasyUnit dimension and errorDimension and its application

  Which pair of physical quantities has the same dimensions?

  Options

  • Option A

    Angular momentum and Planck's constant

  • Option B

    Torque and moment of inertia

  • Option C

    Impulse and surface tension

  • Option D

    Momentum and work done

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  JEE Mains 2025 29 Jan Morning Shift

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• MCQmediumUnit dimension and errorDimension and its application

  The quantity √(ε₀/μ₀), where ε₀ is permittivity and μ₀ is permeability of free space, has dimensions of:

  Options

  • Option A

    Conductance

  • Option B

    Resistance

  • Option C

    Velocity

  • Option D

    Capacitance

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• MCQeasyUnit dimension and errorDimension and its application

  A quantity X depends on acceleration a, density ρ and force F. Which combination has dimensions of length?

  Options

  • Option A

    F/(ρa)

  • Option B

    √(F/(ρa))

  • Option C

    (F/(ρa))¹ᐟ⁴

  • Option D

    ρa/F

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