On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct: a) y = a sin 2πt/T b) y = a sin vt c) y = a/T sin (t/a) d) y = a√2 [sin (2 πt/T) – cos (2πt/T)]
Correct options are B) and C) b.,c.: In option (a) and (d) the dimensions of y and a in L.H.S. and R.H.S. are equal to L and while in option (b) angle is v.t (where v is velocity) ∴ dimension of v.t is [LT−1][T]=[L]. So sinvt is not dimensionless so option (b) is wrong. In option (c) in R.H.S. dimension of amplitude Ta=[T][L]=[LT−1] which not equal to the dimension of y i.e L and angle at=[L][T]=[LT−1] is not dimensionless. Hence, verifies the option (b) and (c).
