question_answer 14)

A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion : (i)               (ii) (iii)              (iv)   (a = maximum displacement of the particle,  speed of the particle, T= time-period of motion). Rule out the wrong formula on dimensional grounds.  

Answer:

Dimensions of LHS in all the cases (i) to (iv) = L Dimensions of RHS in different cases are as follows:. (i)   (Angle  is dimensionless) This relation is dimensionally correct. (ii)   (Angle is not dimensionless) This relation is dimensionally wrong. (iii)   (Angle is not dimensionless) This relation is dimensionally wrong. (iv)   (Angle is dimensionless) This relation is dimensionally correct. Hence formulae (ii) and (iii) are dimensionally wrong.