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 2π t/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 formulas on dimensional grounds.
NCERT Solutions for Class 11 Physics Part 1 Chapter 2 Exercise 14




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   t :  time  = T
  Time period = T
  velocity :  L / T
  a = displacement = L
 y = displacement = L

a)  L = L Sin L/L          this is okay...
b)   L = L sin  L/T * T  = L Sin L    ... this is not alright, as L is not radians.. Argument of Sine function should be in radians and dimensionless.
c)  L = L/T  Sin T/L        not correct
d)   L = L  (Sin  T/T  + Cos  T/T)          this is alright...

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