Physics

Gravitation and Center of Mass

369 Questions

Gravitation and center of mass questions explore gravitational fields, planetary density, and the mechanics of celestial bodies. Test items include calculating gravitational strength on different planets and understanding the Roche Limit. This topic is essential for the physics syllabus of major competitive exams.

Gravitational fieldCenter of massPlanetary densityHill SphereSpace-time curvature

Gravitation and Center of Mass Questions

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

Moon is a satellite of the Earth, but weightlessness is not experienced at the surface of the Moon because

  1. its distance from the Earth is more.

  2. it is a natural satellite.

  3. its size is big but density is very low.

  4. its own mass is more.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As Moon has its mass, thus it posses its own gravity ($\frac {1}{6}$th of that of the Earth). Hence, weightlessness is not experienced at the surface of the Moon.

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 pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

The atmospheric pressure and height of barometer column is $10^5 P _a$ and 760mm respectively on the earth surface. If the barometer is taken to moon then column height will be

  1. zero

  2. 76 mm

  3. 126.6 mm

  4. 760 mm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since there is no atmosphere on moon, no atmospheric pressure will be there and hence corresponding to 0 pressure, height of mercury column will be 0.


Answer is option A.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

Let $F _{1}$ be the magnitude of the gravitational force exerted on the Sun by Earth and $F _{2}$ be the magnitude of the force exerted on Earth by the Sun. Then.

  1. $F _{1}$ is much greater than $F _{2}$
  2. $F _{1}$ is slightly greater than $F _{2}$
  3. $F _{1}$ is equal to $F _{2}$
  4. $F _{1}$ is slightly less than $F _{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. Therefore, the gravitational force exerted by the Sun on the Earth is equal in magnitude to the force exerted by the Earth on the Sun.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

The mass of the moon is about $1.2$% of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth

  1. Is the same

  2. Is smaller

  3. Is greater

  4. Varies with its phase
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Answer is A.

By Newton's Third Law and Newton's Law of Universal gravitation, the gravitational force the Earth exerts on the Moon is exactly the same as the force the Moon exerts on the Earth. 
F (Earth) = F (Moon)
However, the tidal forces are not equal - the Moon exerts a greater tidal force because tidal forces result from a difference in force across the object. Because the Earth has a greater diameter, the difference in the lunar force across the Earth will be greater than the difference that the terrestrial force exerts across the lunar diameter.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

The gravitational force between two bodies is

  1. repulsive at large distances

  2. attractive at all places

  3. attractive at short distances

  4. repulsive at short distances
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Gravitation is a natural phenomenon by which all things with mass are brought towards one another. It is an attractive force and behaves uniformly for all values of $r$ (distance between the two bodies).

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

On the surface of the earth, force of gravitational attraction between two masses kept at distance d apart is 6 Newtons. If these two masses are taken to the surface of the moon and kept at the same distance d, the force between them will be

  1. 1N

  2. 36N
  3. $\frac { 1 }{ 6 } $N

  4. 6N
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Gravitational force by Newton's law must remain the same.


hence, $(D)$ is correct.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

Gravitational unit of force produce an acceleration in a body equal to 

  1. $g$
  2. $0$
  3. $2g$

  4. unit value
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Acceleration due to gravity is denoted by '$g$'.
A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called gravitational unit of force.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

If the gravitational force of earth suddenly disappears, then which of the following is correct?

  1. weight of the body is zero

  2. mass of the body is zero

  3. both mass and weight become zero

  4. neither the weight nor the mass is zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mass = $m$

Acceleration due to gravity = $g$
Weight of a body is given by, $(W) = m\times g$
When gravitational force disappears $g$ becomes zero, but the mass remains the same.
So, $W = m\times g=m\times 0$ 
Hence, $W = 0$
Correct option will be $(A)$

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

Two identical particles of mass m are placed at a distance r from each other. If their separation is doubled, then the effect on gravitational constant will be 

  1. Gravitational constant remains same

  2. Gravitational constant becomes quadrupled

  3. Gravitational constant becomes 1/4th the actual one

  4. Gravitational constant becomes doubled
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravitational constant does not depend on masses, distances between them

Changing the distance between the masses, decreases the force between them, so that $Fr^2$ remains the same

The correct option is (a)