Physics · Science General

Escape Velocity and Rockets

92 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 satellite orbiting close to the earth's surface will escape if 

  1. its speed is increased by 41.4%

  2. its KE is made 1.5 times the original value
  3. its original speed is increased $\sqrt{1.5}$ times

  4. its stops moving in the orbit
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Escape velocity v_e = sqrt(2) * v_o, where v_o is orbital velocity. v_e = 1.414 * v_o. To escape, the speed must increase by 0.414 * v_o, which is 41.4%.

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

What is the approximate velocity of the solar wind near Earth's orbit?

  1. 100 km/s

  2. 500 km/s

  3. 1000 km/s

  4. 2000 km/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The solar wind typically travels at speeds of around 500 km/s near Earth's orbit.

Multiple choice

What is the approximate mass-loss rate of the solar wind?

  1. 10^8 kg/s

  2. 10^9 kg/s

  3. 10^10 kg/s

  4. 10^11 kg/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The solar wind typically has a mass-loss rate of around 10^9 kg/s.

Multiple choice

What is the approximate mass-loss rate of the solar wind?

  1. 10^8 kg/s

  2. 10^9 kg/s

  3. 10^10 kg/s

  4. 10^11 kg/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The solar wind typically has a mass-loss rate of around 10^9 kg/s.

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 typical speed of a meteor as it enters Earth's atmosphere?

  1. 10-20 km/s

  2. 20-30 km/s

  3. 30-40 km/s

  4. 40-50 km/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Meteors typically enter Earth's atmosphere at speeds ranging from 20 to 30 kilometers per second.

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 typical speed of a meteor as it enters the Earth's atmosphere?

  1. 10-20 km/s

  2. 20-30 km/s

  3. 30-40 km/s

  4. 40-50 km/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The typical speed of a meteor as it enters the Earth's atmosphere is 20-30 km/s.

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.