Question

In a rocket of mass, fuel is consumed at a rate of $40kg/s$. The velocity of the gases ejected from the rocket is $5x{10}^{4}m/s$, the thrust on the rocket is:

• A. $2x{10}^{3}N$
• B. $2.5m/s^2$
• C. $2x{10}^{6}N$
• D. $2x{10}^{9}N$

Answer 1

The correct option is C

$2x{10}^{6}N$

Step 1:Given

The rate of change of mass of the rocket due to the consumption of fuel is $\frac{dm}{dt}=40kg/s$

The velocity of the gases ejected from the rocket $v=5x{10}^{4}m/s$

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,

$\therefore F=ma=m\frac{dv}{dt}=v\frac{dm}{dt}$

Step 3:Calculate the thrust on the rocket:

Upon substituting the values we get,

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

$=200\times {10}^4$

$=2\times {10}^{6}N$

Hence, the correct answer is option (C).