Question

A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion?

(a) y = a sin 2πt/T

(b) y = a sin vt

(c) y = (a/T) sin t/a

(d) y = (a/√2) (sin 2πt/T + cos 2πt/T)

(a = maximum displacement of the particle, v = speed of the particle, T = time period of motion). Rule out the wrong formulae on dimensional grounds.

Answer 1

The argument of a trigonometric function,i.e., angle is dimensionless.

(a) [2πt/T] = [M⁰L⁰T⁰]

∴ |y| = |a|. So it is correct.

(b) vt is not dimensionless. So, it is wrong.

(c) t/a is not dimensionless,So,it is wrong.

(d) 2πt/T is dimensionless, So,it is correct