Tag: weightlessness

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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.