Q. 144.0( 29 Votes )

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/T

B. y = a sin vt

C. y = (a/T) sin t/a

D.

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

Answer :

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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