# A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion:A. y = a sin 2 t/TB. y = a sin vtC. y = (a/T) sin t/aD. (a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.

The dimensions of the quantities involved are:

y = M0L1T0

a = M0L1T0

T or t=T

A. correct

Explanation: t/T is unitless. Therefore, dimension of y should be the dimension of a which is true.

B. incorrect

Explanation: quantities inside the trigonometric expressions should be unitless but dimension of vt = M0L1T0 which is having unit of length and is therefore wrong.

C. incorrect

Explanation: quantities inside the trigonometric expressions should be unitless but dimension of t/a = M0L-1T1 which is having unit of time/length and is therefore wrong.

D. correct

Explanation: t/T is unitless. Therefore, dimension of y should be the dimension of a which is true.

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