A student writes four different expression for the displacement `y` in a period motion
`y = a sin"(2 pi r)/(T)`
`y = a sin vt`
`y = (a)/(t) sin"(t)/(a)`
`y = (a )/(sqrt(2))[sin'(2 pi r)/(T)+ cos '(2 pi r)/(T)]`
where `a` is maximum displacement , x is the speed and T is the time period then dimensionally.

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 book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain peroidic motion : (a) y = asin2pi t//T (b) y=asinvt ("c") y=(a//T) sin t//a (d) y=(a//sqrt2) (sin 2pi t//T + cos 2pit//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)

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain peroidic motion : (a) y = asin2pi t//T (b) y=asinvt ("c") y=(a//T) sin t//a (d) y=(a//sqrt2) (sin 2pi t//T + cos 2pit//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)

A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae (a) y = a sin (2pi)/(T)t (b) y = a sin vt (c) y = a/T sin (t/a) (d) y = a/T (sin (2pi)/(T) t + cos (2pi)/(T) t)