Tag: gravitation: planets and satellites

Questions Related to gravitation: planets and satellites

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

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

  1. $\displaystyle W _{1}=W _{2}$

  2. $\displaystyle W _{1}< W _{2}$

  3. $\displaystyle W _{1}>W _{2}$

  4. $\displaystyle W _{1}\neq W _{2}$

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Correct Option: A
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, ${ W } _{ 1 }={ W } _{ 2 }$.

A 60kg man goes around the earth in a satellite. In the satellite, his weight will be

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

  1. 60 N

  2. 60 Kg

  3. 600 N

  4. Zero

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Correct Option: D
Explanation:

The gravitational force acting on the man in the satellite will be zero as there is no gravitational pull on man in the space hence his weight will be zero.

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

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

  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.

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Correct Option: C
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.

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?

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

  1. Zero

  2. $0.25\ g$

  3. $0.5\ g$

  4. $0.75\ g$

  5. $1\ g$

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Correct Option: A
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.

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.

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

  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. $\displaystyle 4\pi\sqrt{\displaystyle\frac{g}{R}}$

Show answer
Correct Option: A
Explanation:

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

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

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.

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

  1. $8\pi\sqrt{\displaystyle \frac{R}{g}}$

  2. $8\pi\sqrt{\displaystyle \frac{g}{R}}$

  3. $\pi\sqrt{\displaystyle \frac{R}{g}}$

  4. $4\pi\sqrt{\displaystyle \frac{g}{R}}$

Show answer
Correct Option: C
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 }  } $

An astronaut feels weightlessness inside an artificial satellite, because.

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

  1. The satellite is in circular orbit so die to centripetal force the astronaut feel so.

  2. The total mechanical energy of the satellite is negative

  3. At that altitude the acceleration due to gravity is zero

  4. He experiences no force

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Correct Option: D

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.

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

  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

Show answer
Correct Option: A
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.