physics

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1.The potiential energy of a particle varies with distance x from a fixed origin as v=A√x/x+B where A and B are constants.Find the dimensions of AB.
2.The refractive index of a material is given by the equation ʯ=A+B/ʎsquare where A and B are constants,ʎ is wavelength.Then find the dimensional formula for B.
3.A force is given by f=at+btsquare where t is time, what are the dimensions of a and b.

  • physics -

    1. If the expression is U=(A•√x)/(B+x), then
    [B] = m =MLºTº,
    A•√m/m=J.
    [A]=J•m/√m=J•√m=kg•m²•m½/s² =kg•m^(5/2)/s²=ML^(5/2) T^-2

    2. [A] and [n] are dimensionless,
    [B] =m² =MºL²Tº.
    3.
    f=At+Bt²

    [A]=N/s=kg•m/s²•s= kg•m/s ³= MLT^-3,
    [B]=N/s²= MLT^-4.

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