A book with many printing errors contains four different forumlae for the displacement y of a particle undergoing a certain periodic motion : (i) `y = a sin (2pi t)/(T)` (ii) `y = a sin upsilon t` (iii)`y = (a)/(T) sin (t)/(a)` (iv)`y= (a)/(sqrt2)[sin(2pi t)/(T) + cos (2pi t)/(T)]` Here, a is maximum displacement of particle, `upsilon` is speed of particle, T is time period of motion. Rule out the wrong forumlae on dimensinal grounds.
A. `y = A sin (2pi t//T)`
B. `y = A sin (Vt)`
C. `y = A//T sin(t//A)`
D. `y = (A)/(sqrt(2)) (sin omega t + cos omega t)`