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    4.

    A physicist uses dimensional analysis to derive an expression for the energy (E) of a particle based on its mass (m), velocity (v), and Planck's constant (h). They arrive at E=mv2E = mv^2. Why is this result incomplete?

    A

    Dimensional analysis cannot account for dimensionless quantities like the fine-structure constant, which might be involved in a more complex relationship.

    B

    Planck's constant is not relevant for the energy of a classical particle, invalidating the analysis.

    C

    Dimensional analysis cannot handle situations involving both mass and velocity.

    D

    The correct expression involves a logarithmic relationship, which dimensional analysis cannot capture.

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    10.

    A block is projected up a rough inclined plane with an initial velocity uu. The coefficient of kinetic friction between the block and the plane is μk\mu_k. The block travels a distance ss up the plane before coming to rest. What is the angle of inclination hetaheta of the plane?

    A

    \sinheta+μk\cosheta=2gsu2\sinheta + \mu_k\cosheta = \frac{2gs}{u^2}

    B

    \sinhetaμk\cosheta=u22gs\sinheta - \mu_k\cosheta = \frac{u^2}{2gs}

    C

    \sinheta+μk\cosheta=u2gs\sinheta + \mu_k\cosheta = \frac{u^2}{gs}

    D

    \sinheta+μk\cosheta=u22gs\sinheta + \mu_k\cosheta = \frac{u^2}{2gs}

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