1.

    A physical quantity of the dimensions of length that can be formed out of c,  G  and  e24πε0c,\;G{\rm{ \;and \;}}\frac{{{e^2}}}{{4\pi {\varepsilon _0}}} is[ is cc velocity of light, GG is universal constant of gravitation and ee is charge]

    A

    1cGe24πε0\frac{1}{c}G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}

    B

    1c2[Ge24πε0]12\frac{1}{{{c^2}}}{\left[ {G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

    C

    c2[Ge24πε0]12{c^2}{\left[ {G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

    D

    1c2[e2G4πε0]12\frac{1}{{{c^2}}}{\left[ {\frac{{{e^2}}}{{G4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

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    Related Questions

    1.

    A physical quantity of the dimensions of length that can be formed out of c,  G  and  e24πε0c,\;G{\rm{ \;and \;}}\frac{{{e^2}}}{{4\pi {\varepsilon _0}}} is[ is cc velocity of light, GG is universal constant of gravitation and ee is charge]

    A

    1cGe24πε0\frac{1}{c}G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}

    B

    1c2[Ge24πε0]12\frac{1}{{{c^2}}}{\left[ {G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

    C

    c2[Ge24πε0]12{c^2}{\left[ {G\frac{{{e^2}}}{{4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

    D

    1c2[e2G4πε0]12\frac{1}{{{c^2}}}{\left[ {\frac{{{e^2}}}{{G4\pi {\varepsilon _0}}}} \right]^{\frac{1}{2}}}

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    2.

    The dimensions of   ab\;\frac{a}{b} in the equation p=a    t2bxp = \frac{{a\; - \;{t^2}}}{{bx}} where p is pressure, x is distance and t is time, are

    A

    [M2LT3]\left[ {{{\rm{M}}^2}{\rm{L}}{{\rm{T}}^{ - 3}}} \right]

    B

    [MT2]\left[ {{\rm{M}}{{\rm{T}}^{ - 2}}} \right]

    C

    [LT3]\left[ {{\rm{L}}{{\rm{T}}^{ - 3}}} \right]

    D

    [ML3T1]\left[ {{\rm{M}}{{\rm{L}}^3}{{\rm{T}}^{ - 1}}} \right]

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    4.

    The dimension of k in the equation W=12kx2W = \frac{1}{2}k{x^2} is

    A

    [ML0T2]\left[ {{\rm{M}}{{\rm{L}}^0}{{\rm{T}}^{ - 2}}} \right]

    B

    [M0LT1]\left[ {{{\rm{M}}^0}{\rm{L}}{{\rm{T}}^{ - 1}}} \right]

    C

    [MLT2]\left[ {{\rm{ML}}{{\rm{T}}^{ - 2}}} \right]

    D

    [ML0T1]\left[ {{\rm{M}}{{\rm{L}}^0}{{\rm{T}}^{ - 1}}} \right]

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    6.

    The refractive index of a material is given by the equation n=A  +Bλ2,n = \frac{{A\; + B}}{{{\lambda ^2}}},, where A and B are constant. The dimensional formula for B is

    A

    [M0L2T1]\left[ {{{\rm{M}}^0}{{\rm{L}}^2}{{\rm{T}}^{ - 1}}} \right]

    B

    [M0L2T0]\left[ {{{\rm{M}}^0}{{\rm{L}}^{ - 2}}{{\rm{T}}^0}} \right]

    C

    [M0L2T2]\left[ {{{\rm{M}}^0}{{\rm{L}}^2}{{\rm{T}}^{ - 2}}} \right]

    D

    [M0L2T0]\left[ {{{\rm{M}}^0}{{\rm{L}}^2}{{\rm{T}}^0}} \right]

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    7.

    Given that :y=Asin[(2πλ)  (ctx)]:y = A\sin \left[ {\left( {\frac{{2\pi }}{\lambda }} \right)\;\left( {ct - x} \right)} \right] where, y and x are measured in metre. Which of the following statements is true?

    A

    The unit of λ\lambda is same as that of x and A

    B

    The unit of λ\lambda is same as that of x but not of A

    C

    The unit of c is same as that of 2πλ\frac{{2\pi }}{\lambda }

    D

    The unit of (ct-x) is same as that of 2πλ\frac{{2\pi }}{\lambda }

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