(B) The thrust force exerted on the rocket is given by $F_{thrust} = v_{rel} \left( \frac{dm}{dt} \right)$.Given $v_{rel} = 400 \, m/s$ and $\frac{dm}

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(B) The thrust force exerted on the rocket is given by $F_{thrust} = v_{rel} \left( \frac{dm}{dt} \right)$.Given $v_{rel} = 400 \, m/s$ and $\frac{dm}{dt} = 5 \, kg/s$,the thrust force is $F_{thrust} = 400 \times 5 = 2000 \, N$.The net force on the rocket is $F_{net} = F_{thrust} - mg$.Using Newton's second law,$ma = F_{thrust} - mg$,so $a = \frac{F_{thrust}}{m} - g$.Substituting the values: $a = \frac{2000}{100} - 10 = 20 - 10 = 10 \, m/s^2$.

Class 11 Physics Laws of Motion Variable Mass System and Rocket Problem

Medium

At a certain instant of time,the mass of a rocket going up vertically is $100 \, kg$. If it is ejecting $5 \, kg$ of gas per second at a speed of $400 \, m/s$,the acceleration of the rocket would be ........ $m/s^2$ (taking $g = 10 \, m/s^2$).

A
$20$
B
$10$
C
$2$
D
$1$

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Variable Mass System and Rocket Problem

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At a certain instant of time,the mass of a rocket going up vertically is $100 \, kg$. If it is ejecting $5 \, kg$ of gas per second at a speed of $400 \, m/s$,the acceleration of the rocket would be ........ $m/s^2$ (taking $g = 10 \, m/s^2$).

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Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times, whereas its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

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The motion of a rocket in an upward direction with high speed is based on the principle of conservation of:

$A$ rocket of initial mass $6000 \ kg$ ejects gases at a constant rate of $16 \ kg/s$ with a constant relative speed of $11 \ km/s$ in gravity-free space. What is the acceleration of the rocket $1 \ min$ after the blast? (in $m/s^2$)

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