1. Tardigrade
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  4. 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 .

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Q. 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 ____.

Physical World, Units and Measurements

Solution:

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