Energy of the system as a function of time, E(t)=αt−βt3 Where, α and β are constant. According to principle of homogenity, dimension of αt= dimension of energy i.e ⇒[α][t]=[E] ⇒[α][T]=[ML2T−2] ⇒[α]=[ML2T−3] Again, dimension of βt3= dimension of energy ⇒[β][t3]=[ML2T−2] ⇒[β][T3]=[ML2T−2] ⇒[β]=[ML2T−5]