A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion. 1. y= asin""(2pit)/(T) 2. y= asinvt 3. y= (a)/(T)sin""(t)/(a) 4. y= (asqrt(2))(sin((2pit)/(T))+ cos((2pit)/(T))) where a is the maximum displacement of the particle, v is the speed of the particle, T is the time period of motion. Then dimensionally

A book with many printing errors contains four different formulae for

1.	A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion. 1. y= asin""(2pit)/(T) 2. y= asinvt 3. y= (a)/(T)sin""(t)/(a) 4. y= (asqrt(2))(sin((2pit)/(T))+ cos((2pit)/(T))) where a is the maximum displacement of the particle, v is the speed of the particle, T is the time period of motion. Then dimensionally
Answer» 1 and 2 are WRONG 2 and 3 are wrong 3 and 4 are wrong 1 and 4 are wrong Solution :Since LHS is DISPLACEMENT, so RHS should have dimensions of displacement. Also argument of a trigonometric function should be dimensionless. In (2) argument is not dimensionless. In (3) argument is not dimensionless and `(a)/(T)` has not dimension of displacement. THEREFORE (2) and (3) are dimensionally wrong.