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Standard VII

Physics

Bernoulli's Principle

The thrust de...

Question

The thrust developed by a rocket motor is given by $F = m v + A (P_{1} - P_{2})$ 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:

dimensionally correct

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dimensionally wrong

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some times correct and some times wrong

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algebrically correct

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Solution

The correct option is D dimensionally wrong
$F = m v + A (P_{1} - P_{2})$
Now, $[F] = [M^{1} L^{1} T^{- 2}]$
and, $[m v] = [M^{1} L^{1} T^{- 1}]$
Also, $[A (P_{1} - P_{2})] = [L^{2} \times (M^{1} L^{- 1} T^{- 2})$ $= [M^{1} L^{1} T^{- 2}]$
The two terms on the RHS of the equation have different dimensions and hence cannot be equated to the term on LHS.
$∵$ $[m v] \neq [F] = [A (P_{1} - P_{2})]$ ,
The equation is dimensionally wrong.

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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:

The thrust developed by a rocket motor is given by $F = m v + A (P_{1} - P_{2})$ 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: