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Math Help - vector analysis problem on dimensions

  1. #1
    jaspal
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    vector analysis problem on dimensions

    Suppose a sphere of radius r is dropped into a viscous liquid of coefficient of viscosity q, and its velocity at an instant is v. The frictional force, F, acting against the sphere is given by
    F=k(r^x)(q^y)(v^z)
    where k is a constant.

    Find,using the method of dimensions, the values of x,y,z.
    Note the dimensions of the coefficient of viscosity are [M][L]^-1[T]^-1.

    My solutions is as follows;

    F=ma=[M][L][T]^-2
    v=[L][T]^-1

    Therefore
    [M][L][T]^-2=k[L]^x.q[M]^y.[L]^-y.[T]^-y.[L]^z.[T]^-z

    so
    [L] 1=X-Y+Z
    [M] 1=Y
    [T]-2=-Y-Z

    and get values x,y,z all equal to 1.

    Is this correct? I will appreciate any responses.
    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jaspal
    Suppose a sphere of radius r is dropped into a viscous liquid of coefficient of viscosity q, and its velocity at an instant is v. The frictional force, F, acting against the sphere is given by
    F=k(r^x)(q^y)(v^z)
    where k is a constant.

    Find,using the method of dimensions, the values of x,y,z.
    Note the dimensions of the coefficient of viscosity are [M][L]^-1[T]^-1.

    My solutions is as follows;

    F=ma=[M][L][T]^-2
    v=[L][T]^-1

    Therefore
    [M][L][T]^-2=k[L]^x.q[M]^y.[L]^-y.[T]^-y.[L]^z.[T]^-z
    Extra q left in the RHS of this last equation.


    so
    [L] 1=X-Y+Z
    [M] 1=Y
    [T]-2=-Y-Z

    and get values x,y,z all equal to 1.

    Is this correct? I will appreciate any responses.
    Thanks.
    Yes this is correct.

    RonL
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