\[(a)\;3.25 \times 10^4 \;N \quad (b)\;2 \times 10^4\;N \quad (c)\; 5.25 \times 10^4\;N \quad (d)\;7.25 \times 10^4 \;N\]

The effective velocity of air entering the compressor is equal to the airplane velocity

$v_i=200 m/s$

Engine exhaust exerts a force to the left= (mass flow rate of fuel -air mixture) $\times$ exhaust velocity

Inlet air exerts force to right= (mass flow of inlet air) \times (inlet velocity)

Mass flow of inlet of air $=\large\frac{dmi}{dt}$

$\qquad=100 kg$

Mass flow of fuel $=\large\frac{dmj}{dt}$$=5 kg$

exhaust velocity $=v_e=500 m/s$

Engine Thrust $T=\bigg(\large\frac{dmi}{dt}+\frac{dmj}{dt}\bigg)$$v_e-\large\frac{dmi}{dt}$$v_i$

$\qquad =(100+5)500-100 \times 200$

$\quad\;=3.25 \times 10^4 N$

Hence a is the correct answer.

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