Question

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

• A. correct
• B. wrong
• C. sometimes wrong, sometimes correct
• D. data is not adequate

Answer 1

The correct option is A correct

Using principle of homogeneity,

$L.H.S=\left[F\right]=\left[M^1{L}^2{T}^{-2}\right]$
$R.H.S=\left[m\right]\left[v\right]+\left[A\right][P_1-P_2]$

$=\left[M^1{L}^0{T}^{-1}\right]\left[M^0{L}^1{T}^{-1}\right]+\left[M^0{L}^2{T}^0\right]\left[M^1{L}^{-1}{T}^{-2}\right]$

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

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

$=L.H.S$