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Work Energy Theorem Application

The energy ...

Question

The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $a$ . Using the method of dimensional analysis find the relation between $E, m, n$ and $a$ .

E = k m n^{2} a^{2}

(

k = a

dimensionless constant)

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E = k m^{2} n^{2} a^{3}

(

k = a

dimensionless constant)

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E = k m^{1} n^{1} a^{2}

(

k = a

dimensionless constant)

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E = k m^{2} n^{1} a^{2}

(

k = a

dimensionless constant)

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Solution

The correct option is A $E = k m n^{2} a^{2}$ ( $k = a$ dimensionless constant)
Dimensions of Energy $E - M L^{2} T^{- 2}$
Dimensions of frequency $n$ - $T^{- 1}$
Dimensions of Amplitude $a$ - $L^{1}$
comparing with dimensions of energy,
Power of $m = 1$ ,
Power of $n = 2$
Power of $a = 2$
Hence, Option A is correct.

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The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude a. Using the method of dimensional analysis find the relation between E,m,n and a.

The correct option is A E=kmn2a2 (k=a dimensionless constant)Dimensions of Energy E−ML2T−2Dimensions of frequency n-T−1Dimensions of Amplitude a -L1comparing with dimensions of energy,Power of m=1,Power of n=2Power of a=2Hence, Option A is correct.

The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $a$ . Using the method of dimensional analysis find the relation between $E, m, n$ and $a$ .