Calculate the dimension of energy for me

Physics

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Answer

The dimension of energy can be derived from its formula. One common formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2.

Step-by-step solution

4 steps

  1. Identify the formula for energy.

    We will use the kinetic energy formula: KE=12mv2KE = \frac{1}{2}mv^2.

  2. Determine the dimensions of each variable.

    • Mass (mm) has dimensions of [M][M].
    • Velocity (vv) has dimensions of [L][T]−1[L][T]^{-1} (length per time).

  3. Substitute the dimensions into the formula.

    The constant 12\frac{1}{2} is dimensionless.
    So, the dimensions of KE are [M]×([L][T]−1)2[M] \times ([L][T]^{-1})^2.

  4. Simplify the expression.

    ([L][T]−1)2=[L]2[T]−2([L][T]^{-1})^2 = [L]^2[T]^{-2}.
    Therefore, the dimensions of energy are [M][L]2[T]−2[M][L]^2[T]^{-2}.

    [Energy]=[M][L]2[T]−2[Energy] = [M][L]^2[T]^{-2}

    The dimension of energy is [M][L]^2[T]^{-2].

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