Rocket Mechanism

Q. A rocket with an initial mass of $1000\text{kg}$ is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of $10\text{kg}$ per second. The burnt matter is ejected vertically downwards with a speed of $2000\text{m/s}$ relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

1. $4000.6\text{m/s}$
2. $2500.4\text{m/s}$
3. $4500.2\text{m/s}$
4. $1232.6\text{m/s}$

Q. A rocket of mass $120\text{kg}$ has $280\text{kg}$ of fuel is ready for the take off. The relative exhaust velocity of the fuel is $1.8\text{km/s}$ and the rate of consumption of the fuel is $2\text{kg/s}$. Calculate the ultimate vertical speed gained by the rocket. (Take $g=9.8{\text{m/s}}^2$)

1. $3.54\text{km/s}$
2. $1.79\text{km/s}$
3. $0.795\text{km/s}$
4. $0\text{km/s}$

Q. A rocket of mass $120\text{kg}$ has $280\text{kg}$ of fuel is ready for the take off. The relative exhaust velocity of the fuel is $1.8\text{km/s}$ and the rate of consumption of the fuel is $2\text{kg/s}$. Calculate the ultimate vertical speed gained by the rocket. (Take $g=9.8{\text{m/s}}^2$)

1. $3.54\text{km/s}$
2. $1.79\text{km/s}$
3. $0.795\text{km/s}$
4. $0\text{km/s}$

Q. In the case of rocket propulsion, choose the correct option(s).

1. Momentum of system (rocket + fuel) always remains constant.
2. Newton's third law is applied.
3. If exhaust velocity and rate of burning of mass is kept constant, then acceleration of the rocket will go on increasing.
4. Newton's second law can be applied.

Q. A rocket is launched by the $PSLV$ in which fuel capacity is $500\text{kg}$. The rocket consumes $2\text{kg}$ fuel in $1\text{s}$. Find the time taken by the rocket to consume $300\text{kg}$ fuel.

1. $150\text{s}$
2. $300\text{s}$
3. $100\text{s}$
4. $50\text{s}$

Q. A rocket of initial mass $m=2000\text{kg}$ is burning fuel at the rate of $20\text{kg/s}$ and ejecting burnt matter with a constant speed of $1000\text{m/s}$ w.r.t the rocket. Find the acceleration of the rocket at $t=10\text{sec}$.
[Take $g=10{\text{m/s}}^2$]

1. $0$
2. $0.55{\text{m/s}}^2$
3. $1.11{\text{m/s}}^2$
4. $2.3{\text{m/s}}^2$

Q. A rocket of initial mass $m=2000\text{kg}$ is burning fuel at the rate of $20\text{kg/s}$ and ejecting burnt matter with a constant speed of $1000\text{m/s}$ w.r.t the rocket. Find the acceleration of the rocket at $t=10\text{sec}$.
[Take $g=10{\text{m/s}}^2$]

1. $0$
2. $0.55{\text{m/s}}^2$
3. $1.11{\text{m/s}}^2$
4. $2.3{\text{m/s}}^2$

Q. A rocket is launched by the $PSLV$ in which fuel capacity is $500\text{kg}$. The rocket consumes $2\text{kg}$ fuel in $1\text{s}$. Find the time taken by the rocket to consume $300\text{kg}$ fuel.

1. $150\text{s}$
2. $300\text{s}$
3. $100\text{s}$
4. $50\text{s}$

Q. A rocket with an initial mass $m=2000\text{kg}$ is launched vertically upwards. The rocket burns fuel at the rate of $20\text{kg/s}$. The burnt material is ejected vertically downwards with a speed of $4000\text{m/s}$ relative to the rocket. If burning stops after $30$ seconds, find the maximum velocity of the rocket. (Take $g=10{\text{m/s}}^2$ )

1. $0\text{m/s}$
2. $4515.9\text{m/s}$
3. $1126.7\text{m/s}$
4. $300\text{m/s}$

Q. A rocket with an initial mass of $1000\text{kg}$ is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of $10\text{kg}$ per second. The burnt matter is ejected vertically downwards with a speed of $2000\text{m/s}$ relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

1. $4000.6\text{m/s}$
2. $2500.4\text{m/s}$
3. $4500.2\text{m/s}$
4. $1232.6\text{m/s}$

Q. A rocket is in gravity free space. A scientist wants the acceleration of the rocket to be $2{\text{m/s}}^2$. Initial mass of the rocket is $1000\text{kg}$ and the speed of ejection of burnt fuel w.r.t the rocket is $500\text{m/s}$. Find the rate of consumption of fuel $\left(\text{in kg/s}\right)$, so that the rocket will have an acceleration of $2{\text{m/s}}^2.$

1. $2\text{kg/s}$
2. $4\text{kg/s}$
3. $3\text{kg/s}$
4. $1\text{kg/s}$

Q. The exhaust velocity of the gases coming out of a rocket is $350\text{m/s}$ w.r.t the rocket. The rocket can burn fuel at a rate of $80\text{kg/s}$. For a successful launch, the desired acceleration of the rocket is $4{\text{m/s}}^2$. What is the initial total mass of this rocket? (Take $g=10{\text{m/s}}^2$)

1. $3000\text{kg}$
2. $2000\text{kg}$
3. $1500\text{kg}$
4. $2500\text{kg}$

Q. Mass of spacecraft varies with time as $m=5000e^{-t}\text{kg}$. Find the rate of fuel ejection after $5\text{s}$. (Take $e=2.718$)

1. $23.7\text{kg/s}$
2. $33.7\text{kg/s}$
3. $337\text{kg/s}$
4. $237\text{kg/s}$

Q. Scientists of $ISRO$ want to achieve a velocity of rocket $100\text{m/s}$ after time $t=5\text{sec}$. Velocity of ejected burnt fuel is $20\text{m/s}$ w.r.t the rocket. What should be the rate of consumption of fuel (approximately) so that the rocket will achieve the desired velocity?
Initial mass of rocket is $2000\text{kg}$. [Take $g=10{\text{m/s}}^2$]

1. $300\text{kg/s}$
2. $400\text{kg/s}$
3. $100\text{kg/s}$
4. $200\text{kg/s}$

Q. In a gravity free space, a spacecraft of mass $10\text{kg}$, having $20\text{kg}$ of fuel is initially at rest. The fuel is ignited and the exhaust velocity is $0.1\text{km/s}$. Then, speed gained by the spacecraft when the fuel is fully consumed is

1. $109\text{km/s}$
2. $10.9\text{km/s}$
3. $109\text{m/s}$
4. $1.09\text{km/s}$

Q. A rocket of mass $20\text{kg}$ has $180\text{kg}$ fuel. The exhaust velocity of the fuel is $1.6\text{km/s}$. Calculate the minimum rate of ejection of fuel so that the rocket may rise from the ground. (Take $g=9.8{\text{m/s}}^2$)

1. $1.225\text{kg/s}$
2. $1.725\text{kg/s}$
3. $2.125\text{kg/s}$
4. $2.425\text{kg/s}$

Q. Mass of spacecraft varies with time as $m=5000e^{-t}\text{kg}$. Find the rate of fuel ejection after $5\text{s}$. (Take $e=2.718$)

1. $23.7\text{kg/s}$
2. $33.7\text{kg/s}$
3. $337\text{kg/s}$
4. $237\text{kg/s}$

Q. In case of a variable mass system, a thrust force of magnitude $\left|V_r\frac{dm}{dt}\right|$ has to be applied on the system, whose mass is changing. Which of the following statements is/are correct?

1. Direction of thrust force is along $V_r$ if the mass is increasing.
2. Direction of thrust force is opposite to $V_r$ if the mass is increasing
3. Direction of thrust force is opposite to $V_r$ if the mass is decreasing.
4. Direction of thrust force is along $V_r$ if the mass is decreasing.

Q. Find the mass $\left(m\right)$ of the rocket as a function of time, if it moves with a constant acceleration $a$ in the absence of external force. The gas escapes with a constant velocity $u$ relative to the rocket and its initial mass was $m_0$.

1. $m=m_0{e}^{-at/u}$
2. $m=m_0{e}^{-t/u}$
3. $m=m_0{e}^{at/u}$
4. $m=m_0{e}^{2at/u}$

Q. Scientists of $ISRO$ want to achieve a velocity of rocket $100\text{m/s}$ after time $t=5\text{sec}$. Velocity of ejected burnt fuel is $20\text{m/s}$ w.r.t the rocket. What should be the rate of consumption of fuel (approximately) so that the rocket will achieve the desired velocity?
Initial mass of rocket is $2000\text{kg}$. [Take $g=10{\text{m/s}}^2$]

1. $300\text{kg/s}$
2. $400\text{kg/s}$
3. $100\text{kg/s}$
4. $200\text{kg/s}$

Q. A rocket of mass $3500\text{kg}$ has to achieve a velocity of $1000\text{m/s}$ over a launch time of $10$ minutes. The nozzle of the rocket is designed to let out exhaust gases at a velocity of $300\text{m/s}$ w.r.t the rocket. What is the amount of fuel that is consumed during the launch?

1. $81660\text{kg}$
2. $66666.66\text{kg}$
3. $90000\text{kg}$
4. $88666.66\text{kg}$