A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae (a) y = a sin (2pi)/(T)t (b) y = a sin vt (c) y = a/T sin (t/a) (d) y =a/T (sin (2pi)/(T) t + cos (2pi)/(T) t)

A book with printing error contains four different formulae for displa

1.	A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae (a) y = a sin (2pi)/(T)t (b) y = a sin vt (c) y = a/T sin (t/a) (d) y =a/T (sin (2pi)/(T) t + cos (2pi)/(T) t)
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :The argument of sine and cosine function must be dimensionaless so (a) is the <a href="https://interviewquestions.tuteehub.com/tag/probable-2213116" style="font-weight:bold;" target="_blank" title="Click to know more about PROBABLE">PROBABLE</a> correct <a href="https://interviewquestions.tuteehub.com/tag/formula-464310" style="font-weight:bold;" target="_blank" title="Click to know more about FORMULA">FORMULA</a>. Since <br/> (a) y = a sin `((2pi)/(T)t), :. [(2pit)/(T)] = [T^(0)]` is dimensionless. <br/> (b) y = a sin vt, `:. [vt] = [T]` is dimensional so this equation is <a href="https://interviewquestions.tuteehub.com/tag/incorrect-499101" style="font-weight:bold;" target="_blank" title="Click to know more about INCORRECT">INCORRECT</a>. <br/> (c) y = `a/t sin (t/a), :. [t/a]` is dimensional so this is incorrect. <br/> (b) y = `a/t (sin ""(2pi)/(T) t + cos""(2pit)/(T))` , Though `(2pit)/(T)` dimensionless `a/T` does not have dimension of displacement so this is also incorrect.</body></html>