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  4. In a rocket, fuel burns at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to

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Q. In a rocket, fuel burns at the rate of $1 \,kg/s$. This fuel is ejected from the rocket with a velocity of $60\, km/s$. This exerts a force on the rocket equal to

AIPMTAIPMT 1994Laws of Motion

Solution:

Rate of burning of fuel $\left(\frac{d m}{d t}\right)=1 \,kg / s$
and velocity of ejected fuel $(v)=60 \,km / s $
$=60 \times 10^{3} m / s$.
Force $=$ Rate of change of momentum
$=\frac{d p}{d t}=\frac{d(m v)}{d t}=v \frac{d m}{d t}$
$=\left(60 \times 10^{3}\right) \times 1=60060\, N .$