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    22.

    The dimensional formula of 1Ξ΅0e2hc\frac{1}{{{\varepsilon _0}}}\frac{{{e^2}}}{{hc}} is

    A

    [M0L0T0A0]\left[ {{{\rm{M}}^0}{{\rm{L}}^0}{{\rm{T}}^0}{{\rm{A}}^0}} \right]

    B

    [Mβˆ’1L3T2A]\left[ {{{\rm{M}}^{ - 1}}{{\rm{L}}^3}{{\rm{T}}^2}{\rm{A}}} \right]

    C

    [ML3Tβˆ’4Aβˆ’2]\left[ {{\rm{M}}{{\rm{L}}^3}{{\rm{T}}^{ - 4}}{{\rm{A}}^{ - 2}}} \right]

    D

    [Mβˆ’1Lβˆ’3T4]\left[ {{{\rm{M}}^{ - 1}}{{\rm{L}}^{ - 3}}{{\rm{T}}^4}} \right]

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    23.

    The dimensional formula of coefficient of permittivity for free space (Ξ΅0)\left( {{\varepsilon _0}} \right) in the equation F=14πΡ0q1q2r2,F = \frac{1}{{4{\rm{\pi }}{\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{r^2}}}, where symbols have their usual meanings, is

    A

    [ML3Aβˆ’2Tβˆ’4]\left[ {{\rm{M}}{{\rm{L}}^3}{{\rm{A}}^{ - 2}}{{\rm{T}}^{ - 4}}} \right]

    B

    [Mβˆ’1Lβˆ’3T4A2]\left[ {{{\rm{M}}^{ - 1}}{{\rm{L}}^{ - 3}}{{\rm{T}}^4}{{\rm{A}}^2}} \right]

    C

    [Mβˆ’1Lβˆ’3Aβˆ’2Tβˆ’4]\left[ {{{\rm{M}}^{ - 1}}{{\rm{L}}^{ - 3}}{{\rm{A}}^{ - 2}}{{\rm{T}}^{ - 4}}} \right]

    D

    [ML3A2Tβˆ’4]\left[ {{\rm{M}}{{\rm{L}}^3}{{\rm{A}}^2}{{\rm{T}}^{ - 4}}} \right]

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    24.

    The constant of proportionality 14πΡ0β€…β€Š\frac{1}{{4{\rm{\pi }}{{\rm{\varepsilon }}_0}}}\; in Coulomb’s law has the following units

    A

    Cβˆ’2Nm2{{\rm{C}}^{ - 2}}{\rm{N}}{{\rm{m}}^2}

    B

    C2Nβˆ’1mβˆ’2{{\rm{C}}^2}{{\rm{N}}^{ - 1}}{{\rm{m}}^{ - 2}}

    C

    C2Nm2{{\rm{C}}^2}{\rm{N}}{{\rm{m}}^2}

    D

    Cβˆ’2Nβˆ’1mβˆ’2{{\rm{C}}^{ - 2}}{{\rm{N}}^{ - 1}}{{\rm{m}}^{ - 2}}

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    26.

    The dimensions of permittivity Ξ΅0{\varepsilon _0} are

    A

    A2T2Mβˆ’1Lβˆ’3{A^2}{T^2}{M^{ - 1}}{L^{ - 3}}

    B

    A2T4Mβˆ’1Lβˆ’3{A^2}{T^4}{M^{ - 1}}{L^{ - 3}}

    C

    Aβˆ’2Tβˆ’4ML3{A^{ - 2}}{T^{ - 4}}M{L^3}

    D

    A2Tβˆ’4Mβˆ’1Lβˆ’3{A^2}{T^{ - 4}}{M^{ - 1}}{L^{ - 3}}

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    27.

    SI unit of permittivity is

    A

    C2m2N2{{\rm{C}}^2}{{\rm{m}}^2}{{\rm{N}}^2}

    B

    C2mβˆ’2Nβˆ’1{{\rm{C}}^2}{{\rm{m}}^{ - 2}}{{\rm{N}}^{ - 1}}

    C

    C2m2Nβˆ’1{{\rm{C}}^2}{{\rm{m}}^2}{{\rm{N}}^{ - 1}}

    D

    Cβˆ’1m2Nβˆ’2{{\rm{C}}^{ - 1}}{{\rm{m}}^2}{{\rm{N}}^{ - 2}}

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    29.

    The physical quantities not having same dimensions are

    A

    Torque and work

    B

    Momentum and Planck’s constant

    C

    Stress and Young’s modules

    D

    Speed and (ΞΌ0Ξ΅0)βˆ’1/2{\left( {{{\rm{\mu }}_0}{{\rm{\varepsilon }}_0}} \right)^{ - 1/2}}

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