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Question: Answered & Verified by Expert
In a rocket of mass $1000 \mathrm{~kg}$ fuel is consumed at a rate of $40 \mathrm{~kg} / \mathrm{s}$. The velocity of the gases ejected from the rocket is $5 \times 10^4 \mathrm{~m} / \mathrm{s}$. The thrust on the rocket is
PhysicsCenter of Mass Momentum and CollisionJEE Main
Options:
  • A $2 \times 10^3 \mathrm{~N}$
  • B $5 \times 10^4 \mathrm{~N}$
  • C $2 \times 10^6 \mathrm{~N}$
  • D $2 \times 10^9 \mathrm{~N}$
Solution:
2718 Upvotes Verified Answer
The correct answer is: $2 \times 10^6 \mathrm{~N}$
$2 x 10^6 \mathrm{~N}$
Step 1:Given
The rate of change of mass of the rocket due to the consumption of fuel is $\frac{d m}{d t}=40 \mathrm{~kg} / \mathrm{s}$
The velocity of the gases ejected from the rocket $v=5 x 10^4 \mathrm{~m} / \mathrm{s}$
Step 2: Formula used
We know that the accelerated mass in a particular direction causes an upthrust force that is equal in magnitude and opposite in direction.
For a changing mass, we get,
$\therefore F=m a=m \frac{d v}{d t}=v \frac{d m}{d t}$
Step 3:Calculate the thrust on the rocket:
Upon substituting the values we get,
$\begin{aligned}
& F=40 \times 5 \times 10^4 \\
& =200 \times 10^4 \\
& =2 \times 10^6 N
\end{aligned}$

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