Tag: weightlessness

Questions Related to weightlessness

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.