Dimension and its application questions with solutions

Showing 1–10 of 91 questions

• MCQeasyUnit dimension and errorDimension and its application

  If G be the gravitational constant and u be the energy density then which of the following quantity have the dimension as that of √(uG):

  Options

  • Option A

    Pressure gradient per unit mass

  • Option B

    Force per unit mass

  • Option C

    Gravitational potential

  • Option D

    Energy per unit mass

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• MCQeasyUnit dimension and errorDimension and its application

  Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

  Options

  • Option A

    Statement I is true but Statement II is false

  • Option B

    Both Statement I and Statement II are false

  • Option C

    Both Statement I and Statement II are true

  • Option D

    Statement I is false but Statement II is true

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• MatchmediumUnit dimension and errorDimension and its application

  Match List I with List II and choose the correct option.

  List 1

  1. Force

  2. Inductive reactance

  3. Electric charge

  4. Dynamic viscosity

  List 2

  1. [ML²T⁻³A⁻²]

  2. [MLT⁻²]

  3. [ML⁻¹T⁻¹]

  4. [AT]

  Options

  • Option A

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

  • Option B

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

  • Option C

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

  • Option D

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

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• MCQmediumUnit dimension and errorDimension and its application

  A force is represented by F = ax² + bt¹ᐟ², where x = distance and t = time. The dimensions of b²/a are:

  Options

  • Option A

    [ML³T⁻³]

  • Option B

    [MLT⁻²]

  • Option C

    [ML⁻¹T⁻¹]

  • Option D

    [ML²T⁻³]

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• MCQeasyUnit dimension and errorDimension and its application

  The dimensions of (Gρ)⁻¹ᐟ², where G is gravitational constant and ρ is density, are:

  Options

  • Option A

    Time

  • Option B

    Length

  • Option C

    Velocity

  • Option D

    Acceleration

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• MCQmediumUnit dimension and errorDimension and its application

  Consider a modified Bernoulli equation.

  P + A ───── Bt² + ρg(h + Bt) + ½ρV² = constant

  If t has the dimension of time then the dimensions of A and B are _____, _____respectively.

  Options

  • Option A

    [ML⁰T⁻¹] and [M⁰LT]

  • Option B

    [ML⁰T⁻¹] and [M⁰LT⁻¹]

  • Option C

    [ML⁰T⁻²] and [M⁰LT⁻²]

  • Option D

    [ML⁰T⁻²] and [M⁰LT⁻¹]

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• MCQeasyUnit dimension and errorDimension and its application

  In the equation P = A + Bt + Ct², P denotes pressure and t time. Dimensions of B and C are:

  Options

  • Option A

    [ML⁻¹T⁻³], [ML⁻¹T⁻⁴]

  • Option B

    [ML⁻¹T⁻²], [ML⁻¹T⁻²]

  • Option C

    [MLT⁻³], [MLT⁻⁴]

  • Option D

    [ML⁻¹T⁻¹], [ML⁻¹T⁻²]

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• MCQeasyUnit dimension and errorDimension and its application

  If E, p, m and c denote energy, linear momentum, mass and speed of light respectively, which relation is dimensionally correct?

  Options

  • Option A

    E²=p²c²+m²c⁴

  • Option B

    E²=pc²+m²c⁴

  • Option C

    E=p²c²+m²c²

  • Option D

    E²=pc²+m²c²

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• MCQmediumUnit dimension and errorDimension and its application

  Given charge q, current I and permeability of vacuum μ₀, which of the following quantities has the dimension of momentum?

  Options

  • Option A

    qμ₀I

  • Option B

    qI/μ₀

  • Option C

    qμ₀/I

  • Option D

    q²μ₀I

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• MCQeasyUnit dimension and errorDimension and its application

  Electric flux φ is related to linear charge density λ and surface charge density σ as φ=αλ+βσ, where α and β have appropriate dimensions. The dimension of β/α is:

  Options

  • Option A

    Displacement

  • Option B

    Area

  • Option C

    Electric field

  • Option D

    Velocity

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