Tag: gravitation: planets and satellites

Quizzes (6) Questions (38)

Questions Related to gravitation: planets and satellites

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

A body is suspended from a spring balance kept in a satellite The reading of the balance is $\displaystyle W _{1}$ when the satellite goes in an orbit of radius $R$ and is $\displaystyle W _{2}$ when it goes in an orbit of radius $2R$ Then

  1. $\displaystyle W _{1}=W _{2}$
  2. $\displaystyle W _{1}< W _{2}$
  3. $\displaystyle W _{1}>W _{2}$
  4. $\displaystyle W _{1}\neq W _{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Answer is A.

The reading on the spring balance is independent of the radius and thus both weight will be the same. Also, there is no gravitational force acting on a satellite.
 
Hence, ${ W } _{ 1 }={ W } _{ 2 }$.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

Consider a satellite going round the earth in a circular orbit. Which of the following statements is wrong?

  1. It is a freely falling body

  2. It is a moving with constant speed.

  3. It is acted upon by a force directed away from the centre of the earth which counter- balances the gravitational pull.

  4. Its angular momentum remains constant.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Satellite going around the earth in circular orbit is in state of free fall, and its speed is constant. speed depends upon the radius of orbit of satellite.

So Its angular velocity($\omega=v\times r$) is also constant and thus angular momentum $m\omega$ is also constant.
Apart from gravitational pull of the earth, there is no other force on the satellite. So option C is incorrect.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

The International Space Station is currently under construction. Eventually, simulated earth gravity may become a reality on the space station. What would the gravitational field through the central axis be like under these conditions?

  1. Zero
  2. $0.25\ g$
  3. $0.5\ g$
  4. $0.75\ g$
  5. $1\ g$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simulated earth gravity can be realized by rotating the space station about a central axis. This rotation creates centrifugal force on the people inside the space station away from the central axis. Thus, $g={ \omega  }^{ 2 }R $ at the central axis $R=0$. So, gravitational field is zero.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

The rotation of the Earth having radius R about its axis speed upto a value such that a man at latitude angle $60^o$ feels weightless. The duration of the day in such case will be.

  1. $\displaystyle 8\pi\sqrt{\displaystyle\frac{R}{g}}$
  2. $\displaystyle 8\pi\sqrt{\displaystyle \frac{g}{R}}$
  3. $\displaystyle \pi\sqrt{\displaystyle\frac{R}{g}}$
  4. $\displaystyle 4\pi\sqrt{\displaystyle\frac{g}{R}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a man at an angle $\theta=60^o$

$T=2\pi\sqrt{\cfrac{R^3}{GM(\cos60^o)}}$
$2\pi \sqrt{\cfrac{R^2}{GM}\cfrac{R}{(\cos 60^o}}$
$2\pi \sqrt{\cfrac{R}{g}\cfrac{1}{1/2}}$
$=8\pi\sqrt{\cfrac{R}{g}}$

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

The rotation of the Earth having radius $R$ about its axis speeds upto a value such that a man at latitude angle $60^o$ feels weightless. The duration of the day in such case will be.

  1. $8\pi\sqrt{\displaystyle \frac{R}{g}}$
  2. $8\pi\sqrt{\displaystyle \frac{g}{R}}$
  3. $\pi\sqrt{\displaystyle \frac{R}{g}}$
  4. $4\pi\sqrt{\displaystyle \frac{g}{R}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$0=g-{ Rw }^{ 2 }\cos ^{ 2 }{ 60° } \ { w }^{ 2 }=\cfrac { 4g }{ R } \quad or,{ w }^{ 2 }=2\sqrt { \cfrac { g }{ R }  } \ \cfrac { 2\pi  }{ T } =2\sqrt { \cfrac { g }{ R }  } \ \therefore T=\pi \sqrt { \cfrac { R }{ g }  } $

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.

and

STATEMENT-2
An object moving around the Earth under the influence of Earths gravitational force is in a state of free-fall.

  1. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

  2. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

  3. STATEMENT -1 is True, STATEMENT-2 is False

  4. STATEMENT -1 is False, STATEMENT-2 is True
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the body to follow circular path, there must be a centripetal force. Here the astronaut is inside a satellite which is revolving around the earth under the influence of earth's gravitation. Thus, the earth's gravitation acts as centripetal force and the net force on astronaut is zero.
Statement 2 is right explanation of 1.