Physics · Science General

Escape Velocity and Rockets

77 Questions

Escape velocity and rockets questions cover spacecraft trajectories and gravitational influences. The topics include calculating maximum velocities and understanding multistage rocket mechanics. These physics concepts are essential for technical exams requiring scientific aptitude.

Escape velocityOrbital mechanicsRocket propulsionAtmospheric entry speedsGravitational pull

Escape Velocity and Rockets Questions

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A particle is projected upward from the surface of earth (radius  $= R$ ) with a speed equal to the orbital speed of a satellite near the earth's surface. The height to which it would rise is

  1. $\sqrt { 2 } R$
  2. $\dfrac { R } { \sqrt { 2 } }$
  3. $R$
  4. $2 R$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} V=\sqrt { \dfrac { { GM } }{ R }  }  \ \frac { { -GMm } }{ R } +\dfrac { 1 }{ 2 } m\left( { \dfrac { { GM } }{ R }  } \right) =\dfrac { { -GMm } }{ { \left( { R+h } \right)  } } +0 \ \Rightarrow \dfrac { { -GMm } }{ R } +\dfrac { { GMm } }{ { 2R } } =\dfrac { { -GMm } }{ { \left( { R+h } \right)  } }  \ \Rightarrow \dfrac { { -GMm } }{ { 2R } } =\dfrac { { -GMm } }{ { \left( { R+h } \right)  } }  \ \Rightarrow 2R=R+h \ \Rightarrow r=R \ Hence, \ option\, \, C\, \, is\, \, correct\, \, answer. \end{array}$

Multiple choice physics force and newton's laws of motion momentum (p) introduction to momentum linear momentum

A rocket is moving at a constant speed in space by burning its fuel and ejecting out the burnt gases through a nozzle. 

There is a change in:

  1. momentum of the rocket

  2. mass of the rocket

  3. both A & B

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As the rocket is moving upward by ejecting gases, its mass is getting decreased gradually. As momentum is the product of the mass and velocity that is $p = m\times v$. Hence momentum decreases as mass is decreasing.

Multiple choice

How does a rocket overcome the force of gravity?

  1. The rocker has engines that push it away from the earth.

  2. The rocket has engines that make it weigh less.

  3. The rocket has engines that pull it toward outer space.

  4. nothing can overcome gravity.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rockets use engines to produce thrust, which is an upward force. When this thrust is greater than the downward force of gravity, the rocket can lift off and accelerate away from the Earth.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

A satellite is revolving in a circular orbit at a height $'h'$ from the earth's surface (radius of earth $R$;$h\ <\ <\ R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to:(Neglect the effect of atmosphere.)

  1. $\sqrt{2gR}$
  2. $\sqrt{gR}$
  3. $\sqrt{gR/2}$
  4. $\sqrt{gR}\left(\sqrt{2}-1\right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

height$=h$

No, the given formula,
Orbital velocity
$v=\cfrac{GM}{R+h}=\cfrac{GM}{R}$ as $h<<R$
Velocity required to escape
$\cfrac{1}{2}mv^{\prime 2}=\cfrac{GMm}{R+h}\v^{\prime}=\cfrac{2GM}{R+h}=\cfrac{2GM}{R}(h<<R)$
$\therefore$ Increase in velocity
$v^{\prime}=v=\sqrt{\cfrac{2GM}{R}}-\sqrt{\cfrac{GM}{R}}\ \quad=\sqrt{2gR}-\sqrt{gR}=\sqrt{gR}(\sqrt2-1)$

Multiple choice

Which astrodynamics concept is used to determine the optimal trajectory for a spacecraft to escape from the gravitational influence of a celestial body, such as Earth?

  1. Hohmann Transfer

  2. Bi-Elliptic Transfer

  3. Gauss's Method

  4. Lambert's Problem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Bi-Elliptic Transfer is an astrodynamics concept used to determine the optimal trajectory for a spacecraft to escape from the gravitational influence of a celestial body, such as Earth, involving two elliptical orbits and two impulsive maneuvers.

Multiple choice

Which differential equation is used to model the motion of a rocket?

  1. Tsiolkovsky Equation

  2. Newton's Second Law

  3. Rocket Equation

  4. Euler's Equations of Motion
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Rocket Equation is used to model the motion of a rocket, taking into account the conservation of mass and momentum.

Multiple choice

What is the significance of the vis-viva equation in interplanetary trajectory analysis?

  1. It relates the spacecraft's velocity to its position in an orbit

  2. It determines the energy required for a spacecraft to escape from a planet's gravitational influence

  3. It calculates the time of flight between two points in an orbit

  4. It predicts the trajectory of a spacecraft under the influence of multiple gravitational forces
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The vis-viva equation is a fundamental equation in orbital mechanics that relates the spacecraft's velocity to its position in an orbit, allowing for the calculation of orbital parameters and energy.

Multiple choice

What is the purpose of an argument of perigee maneuver?

  1. To change the spacecraft's velocity

  2. To change the spacecraft's altitude

  3. To change the spacecraft's inclination

  4. To change the spacecraft's argument of perigee
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Argument of perigee maneuvers are used to change the spacecraft's argument of perigee, which is the angle between the ascending node and the perigee.

Multiple choice

What is the purpose of an argument of perigee maneuver?

  1. To change the spacecraft's velocity

  2. To change the spacecraft's altitude

  3. To change the spacecraft's inclination

  4. To change the spacecraft's argument of perigee
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Argument of perigee maneuvers are used to change the spacecraft's argument of perigee, which is the angle between the ascending node and the perigee.

Multiple choice

What is the velocity required for a spacecraft to escape the gravitational pull of a central body?

  1. Circular velocity

  2. Escape velocity

  3. Orbital velocity

  4. Tangential velocity
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Escape velocity is the minimum velocity required for a spacecraft to overcome the gravitational pull of a central body and achieve an unbound trajectory.

Multiple choice

A rocket is launched vertically from the ground with an initial velocity of 100 m/s. If the acceleration due to gravity is -9.8 m/s^2, what is the maximum height the rocket will reach?

  1. 1020.4 meters

  2. 510.2 meters

  3. 255.1 meters

  4. 127.5 meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We can use calculus to find the velocity and position functions of the rocket, and then determine the maximum height reached.

Multiple choice

A rocket is launched vertically from the ground with an initial velocity of 150 m/s. If the acceleration due to gravity is -9.8 m/s^2, what is the maximum height the rocket will reach?

  1. 1125 meters

  2. 2250 meters

  3. 3375 meters

  4. 4500 meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We can use calculus to find the velocity and position functions of the rocket, and then determine the maximum height reached.

Multiple choice

What is the term used to describe the ratio of the rocket's mass at launch to its mass when all propellants have been consumed?

  1. Specific impulse

  2. Thrust-to-weight ratio

  3. Mass ratio

  4. Payload fraction
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mass ratio of a rocket is the ratio of its mass at launch to its mass when all propellants have been consumed. It is a measure of the rocket's efficiency and is important for determining the payload capacity.

Multiple choice

Which rocket stage is responsible for propelling the rocket through the Earth's atmosphere?

  1. First stage

  2. Second stage

  3. Third stage

  4. Payload fairing
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The first stage of a rocket is responsible for propelling the rocket through the Earth's atmosphere. It is typically the largest and most powerful stage of the rocket and is designed to provide the initial thrust required for liftoff and ascent.