Dimensions of physical quantities

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Question

The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude A as $E = k (m)^{x} (n)^{y} (A)^{z}$ The value of (x + y + z) is___________

Moderate

Solution

By using dimensional analysis
$\begin{array}{l} M L^{2} T^{- 2} = M^{x} {(T^{- 1})}^{y} (L)^{z} = M^{x} L^{z} T^{- y} \\ \Rightarrow x = 1, z = 2, y = 2 \\ \Rightarrow x + y + z = 1 + 2 + 2 = 5 \end{array}$

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