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

1.	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)
Answer» Solution :(ii) `y=asinvt` Here, ANGLE = vt. Its dimensional formula should be `M^(0)L^(0)T^(0)` But `[vt]=(M^(0)L^(1)T^(-1))(T^(1))=M^(0)L^(1)T^(0)` HENCE, (ii) is dimensionally incorrect. (iii) `y=(a)/(T)"sin"(t)/(a)` Here `(a)/(T)` should have same dimensional formula as of y(Displacement). `[(a)/(t)]=(M^(0)L^(1)T^(-2))/(T^(1))=M^(0)L^(1)T^(-1)` Hence, (iii) is dimensionally incorrect. (i) and (IV) are dimensionally correct.