Question

The thrust developed by a rocket motor is given by $F=mv+A(P_1-P_2)$ where $m$ is the mass, $v$ is the velocity of gas and $A$ is area of cross section of the nozzle. $P_1,P_2$ are pressures of the exhaust gas and surrounding atmosphere. Then this equation is:

• A. dimensionally correct
• B. some times correct and some times wrong
• C. algebrically correct
• D. dimensionally wrong

Answer 1

Answer: (D)

$F=mv+A(P_1-P_2)$

Now, $\left[F\right]=\left[M^1{L}^1{T}^{-2}\right]$

and, $\left[mv\right]=\left[M^1{L}^1{T}^{-1}\right]$

Also, $\left[A\right(P_1-P_2\left)\right]=[L^2\times (M^1{L}^{-1}{T}^{-2})$ $=\left[M^1{L}^1{T}^{-2}\right]$

The two terms on the RHS of the equation have different dimensions and hence cannot be equated to the term on LHS.

$\because$ $\left[mv\right]\ne \left[F\right]=\left[A\right(P_1-P_2\left)\right]$,

The equation is dimensionally wrong.