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Question

The thrust developed by a rocket motor is given by F=mv+A(P1P2) 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:

A
dimensionally correct
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B
dimensionally wrong
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C
some times correct and some times wrong
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D
algebrically correct
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Solution

The correct option is D dimensionally wrong
F=mv+A(P1P2)
Now, [F]=[M1L1T2]

and, [mv]=[M1L1T1]

Also, [A(P1P2)]=[L2×(M1L1T2) =[M1L1T2]

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(P1P2)],

The equation is dimensionally wrong.


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