Dimensional Analysis and Its Applications questions with solutions

Showing 1–10 of 130 questions

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

  The dimension of ½ ε₀E², where ε₀ is permittivity of free space and E is electric field, is:

  Options

  • Option A

    [M L² T²]

  • Option B

    [M L⁻¹ T⁻²]

  • Option C

    [M L² T⁻²]

  • Option D

    [M L T²]

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

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

  List 1

  1. Resistivity

  2. Kinematic viscosity

  3. Electric flux

  4. Latent heat

  List 2

  1. [L²T⁻¹]

  2. [ML³T⁻³A⁻¹]

  3. [ML³T⁻³A⁻²]

  4. [L²T⁻²]

  Options

  • Option A

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

  • Option B

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

  • Option C

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

  • Option D

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

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

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

  Match List-I with List-II. List-I: (A) Gravitational constant, (B) Gravitational potential energy, (C) Gravitational potential, (D) Acceleration due to gravity. List-II: (I) [LT⁻²], (II) [L²T⁻²], (III) [ML²T⁻²], (IV) [M⁻¹L³T⁻²]. Choose the correct match.

  Options

  • Option A

    A–III, B–II, C–I, D–IV

  • Option B

    A–I, B–III, C–IV, D–II

  • Option C

    A–IV, B–III, C–II, D–I

  • Option D

    A–II, B–IV, C–III, D–I

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

  The potential energy of a particle moving along x-direction varies as V = Px²/(√x + Q). The dimensions of P²/Q are:

  Options

  • Option A

    [M³ᐟ² L¹ᐟ² T⁻³]

  • Option B

    [M¹ᐟ² L T⁻³]

  • Option C

    [M² L¹ᐟ² T⁻⁴]

  • Option D

    [M L² T⁻⁴]

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

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

  If the period T of a satellite depends only on orbital radius r, central mass M and gravitational constant G, dimensional analysis gives:

  Options

  • Option A

    T ∝ √(r³/(GM))

  • Option B

    T ∝ √(GM/r³)

  • Option C

    T ∝ r/(GM)

  • Option D

    T ∝ GM/r³

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

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

  Consider the dimensional relation in which H equals x raised to power p, multiplied by ε raised to power q, multiplied by E raised to power r, and divided by t raised to power s. Here ε is permittivity, E is electric field, x is distance and t is time. The source paper states H as magnetic field, but its own note says the listed answer is obtained only when H is interpreted as magnetic-field intensity. Under that intended interpretation, what are p, q, r and s, respectively?

  Options

  • Option A

    1, 1, 1, 1

  • Option B

    -1, 1, 2, 1

  • Option C

    1, -1, -2, 1

  • Option D

    -1, -2, -2, 1

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

  The ratio of electric dipole moment to magnetic dipole moment has dimensions Mᴾ$L^{q}$TᴿAˢ. The values of P and Q are:

  Options

  • Option A

    0, -1

  • Option B

    1, -1

  • Option C

    -1, 0

  • Option D

    -1, 1

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