Question

In a rocket of mass $1000$ kg fuel is consumed at a rate of $40kg/s$. The velocity of the gases ejected from the rocket is $5\times {10}^4$. The thrust on the rocket is (in $N$)

• A. $2\times {10}^6$
• B. $2\times {10}^5$
• C. $3\times {10}^6$
• D. $4\times {10}^6$

Answer 1

Answer: (A)

$2\times {10}^6$

Rate of fuel consumption $\frac{dm}{dt}=40kg/s$

Relative velocity of the gases w.r.t rocket $V_{rel}=5\times {10}^{4}m/s$

Thus thrust acting on the rocket $F=\frac{dm}{dt}{v}_{rel}$

$\therefore$ $F=40\times 5\times {10}^4$ $N$

$⟹$ $F=2\times {10}^{6}N$