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Check the correctness of the equation `1/2mv^(2)=mgh`, using dimensions.

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To check the correctness of the equation \(\frac{1}{2}mv^{2} = mgh\) using dimensions, we need to ensure that the dimensions on both sides of the equation are the same. This is based on the principle of dimensional homogeneity. ### Step-by-Step Solution: 1. **Identify the dimensions of each term on the left-hand side (LHS) of the equation: \(\frac{1}{2}mv^{2}\)** - **Mass (m):** The dimension of mass is \([M]\). - **Velocity (v):** Velocity is distance per unit time, so its dimension is \([L T^{-1}]\). ...
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