The thrust developed by a rocket motor is given by F=mv+A(P1−P2) where m is the mass, v is the velocity of gas and A is area of cross section of the nozzle. P1,P2 are pressures of the exhaust gas and surrounding atmosphere. Then this equation is:
and, [mv]=[M1L1T−1]
Also, [A(P1−P2)]=[L2×(M1L−1T−2) =[M1L1T−2]
The two terms on the RHS of the equation have different dimensions and hence cannot be equated to the term on LHS.
∵ [mv]≠[F]=[A(P1−P2)],
The equation is dimensionally wrong.