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» SOLUTION :The argument of sine and cosine function must be dimensionaless so (a) is the PROBABLE correct FORMULA. Since (a) y = a sin `((2pi)/(T)t), :. [(2pit)/(T)] = [T^(0)]` is dimensionless. (b) y = a sin vt, `:. [vt] = [T]` is dimensional so this equation is INCORRECT. (c) y = `a/t sin (t/a), :. [t/a]` is dimensional so this is incorrect. (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.