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How to solve this question? Here the options are given different but acc to dimension analysis, the trignometric values are dimenstionless

How to solve this question? Here the options are given different but acc to dimension analysis, the trignometric values are dimenstionless

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Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Dear student,

Here, do not assume x and a to be displacement or acceleration, respectively. Had this been the case, 1(dimensionless) could not be subtracted from the term\dfrac{x}{a}on the right hand side.

All we can know from this term is that the dimensions of x and a are the same. Also, rightly said, the term insidesin^{-1}must be dimensionless. Hence the dimensions of the right hand side is that ofa^n.

The denominator of the integral term has dimensions of that of x or a. The numerator has that ofx^2ora^2, making the overall term have dimensions of x or a.

Since the dimensions of RHS and LHS must be same, the dimensions ofa^nis equal to that of a. Hence n=1.

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