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Question

# Based on dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct:

A
y = a sin(2πtT)
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B
y = a sin vt
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C
y = aT sin(ta)
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D
y = a2 [sin(2πtT)cos(2πtT)]
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Solution

## The correct option is C y = aT sin(ta)On the basis of “Principle of homogeneity” equal dimension can be added, subtracted or put equal to each other. As y is the displacement of the particle, its unit should be equal to length, a is the amplitude of SHM and trigonometric functions are dimensionless. (a) y = a sin(2πtT) Here (2πtT) is dimensionless and [y]=[a] (b) y = a sin vt Here [vt]=[L1] So trigonometric function is not dimensionless, hence this relation is not correct for simple harmonic motion. (c) y = aT sin(ta) Here (ta) has dimensions so trigonometric function is not dimensionless, and [y]≠[aT] Hence this relation is not correct for simple harmonic motion. (d) y = a√2 [sin(2πtT)−cos(2πtT)] Here (2πtT) is dimensionless and [y]=[a] Final Answer: (b),(c)

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