Physics

Gravitation and Center of Mass

368 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.

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Gravitation and Center of Mass Questions

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

The unit of gravitational field is 

  1. $\dfrac{N}{kg}$
  2. $\dfrac{N}{s}$
  3. $\dfrac{kg}{s^2}$
  4. $\dfrac{N}{kg m^2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The gravitational field is the region in which the gravitational force can be experienced or its presence can be felt. The intensity of gravitational force is the force acting on a unit mass of a body. The gravitational field is mathematically given by, gravitational force divided by the mass of the body. And the unit of the gravitational field is the ratio of the unit of force to that of mass, that is, $N/kg$.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

What is gravitational field?

  1. A gravitational field is a region where any other body that has mass will experience a force of attraction.

  2. A gravitational field is a region where any other body that has mass will experience a force of repulsion.

  3. A gravitational field is a region where any other body that has mass will experience no force of attraction.

  4. A gravitational field is a region where any other body that has mass will experience no force of repulsion.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Point A is the definition of the gravitational field. 

Gravitational force is always attractive in nature and hence there is no question of repulsion.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Which of the following option is/are correct?

  1. If acting at a single point, the gravitational force on an extended object can be treated as its centre of gravity

  2. If the gravitational field is nonuniform across the object then it can be treated as its centre of mass.

  3. If acting at multiple point, the gravitational force on an extended object can be treated as its centre of gravity

  4. If the gravitational field is uniform across the object then it can be treated as its centre of mass.
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

The gravitational force on an extended object can be treated as its center of gravity when acted on a single point. Also, it is uniform across its center of mass.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Determine the gravitational force of two particle of mass $3kg$ and $7 kg$ separated by a distance $2m$.

  1. $35 \times 10^{-11} N$
  2. $25 \times 10^{-11} N$
  3. $5 \times 10^{-11} N$
  4. $3.5 \times 10^{-11} N$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Gravitational force of two particle of mass $3kg$ and $7kg$ separated by a distance $2m$ is given by: 
$F=G\dfrac{Mm}{r^2} = 6.674× 10^{-11} \times \dfrac{ 3 \times 7}{2^2}=35 \times 10^{-11} N$
Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

How far from the centre of the Moon is the Earth-Moon neutral point, where the Earth and the Moon's gravitational field strengths are equal in magnitude but opposite in direction?

$ M _E= 6.0 \times 10^{24} kg \ \ \  M _M = 7.4 \times 10^{22} kg$
The radius of Moon's orbit (assumed to be circular) is: $3.8\times 10^{8} m$.

  1. $3.8 \times 10^{2} m$
  2. $38 \times 10^{6} m$
  3. $38 \times 10^{4} m$
  4. $28 \times 10^{6} m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Strength of gravity $\cfrac { Gm }{ { r }^{ 2 } } $

Let ${ g } _{ e }$ be the value of $Gm$ of earth $=4\times { 10 }^{ 14 }\cfrac { { m }^{ 3 } }{ { s }^{ 2 } } $
      ${ g } _{ m }$ be the value of $Gm$ of moon $=5\times { 10 }^{ 12 }\cfrac { { m }^{ 3 } }{ { s }^{ 2 } } $
Let $d\rightarrow$distance between earth and moon $=380\times { 10 }^{ 6 }m$
Let equilibirum point from earth be at a distanexe :- $x$
       $\cfrac { { g } _{ e } }{ { x }^{ 2 } } =\cfrac { { g } _{ m } }{ { \left( d-x \right)  }^{ 2 } } $
      ${ g } _{ e }\left( { x }^{ 2 }-2xd+{ d }^{ 2 } \right) ={ g } _{ m }{ x }^{ 2 }\ \left( { g } _{ e }-{ g } _{ m } \right) { x }^{ 2 }-{ 2dg } _{ e }x+{ d }^{ 2 }{ g } _{ e }=0$
Solving the quadratic formula
$x=\cfrac { { 2dg } _{ e }\pm \sqrt { 4{ d }^{ 2 }{ g } _{ e }^{ 2 }-{ 4d }^{ 2 }{ g } _{ e }\left( { g } _{ e }-{ g } _{ m } \right)  }  }{ 2\left( { g } _{ e }-{ g } _{ m } \right)  } =\cfrac { { dg } _{ e }\pm d\sqrt { { g } _{ e }{ g } _{ m } }  }{ { g } _{ e }-{ g } _{ m } } \approx 342\times { 10 }^{ 6 }m$
$\therefore$ Distance from moon :-$d-x=38\times { 10 }^{ 6 }m$

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Gravitational field is directed

  1. towards the earth

  2. away from earth

  3. has no direction

  4. in a specific direction making angle with earth
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Force if gravity on an object due to Earth always act towards the Earth as it is attractive in nature. Therefore, when an object us thrown up, the force of gravity acts towards the Earth. 

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Due to a mass distribution, the gravitational field is $\dfrac{k}{x^3} $ along x-axis where $k$ is a constant. If the gravitational potential is taken to be at infinity, then the gravitational potential at $x$ is 

  1. $\dfrac{k}{x}$
  2. $\dfrac{k}{2x^2}$
  3. $\dfrac{k}{x^4}$
  4. $\dfrac{k}{x^6}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$V=-\int { Edx } =-\int { \cfrac { K }{ { x }^{ 3 } } dx=K\left( \cfrac { 1 }{ 2{ x }^{ 2 } }  \right)  } =\cfrac { K }{ { 2x }^{ 2 } } $

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

The gravitational intensity is denoted by :

  1. $g$
  2. $G$
  3. $E$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravitational intensity is a vector quantity related to the condition at any point under gravitational influence the measure of which is the gravitational force exerted upon a unit mass placed at the point in question. It is denoted by $g.$ 

$g = GM/$$R^2$, where $M$ is the mass of earth and $R$ is the radius of earth.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

A gravitational field is

  1. a field of gravitons

  2. a field of massive particles

  3. the force field that exists in the space around every mass or group of masses.

  4. Force exerted on an unit charge
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Gravitational field is the force field that exists in the space around every mass or group of masses. Mathematically, it is F/m

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

If the distance between two particles is reduced to half, the gravitational attraction between them will be

  1. Halved

  2. Quadrupled

  3. Doubled

  4. Reduced to a quarter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Gravitational force $=\dfrac { G{ m } _{ 1 }{ m } _{ 2 } }{ { r }^{ 2 } } ={ F } _{ 1 }$

If distance made $0$ half of original value
${ F } _{ 2 }=\dfrac { G{ m } _{ 1 }{ m } _{ 2 } }{ { \left( \dfrac { r }{ 2 }  \right)  }^{ 2 } } $
${ F } _{ 2 }=\dfrac { 4G{ m } _{ 1 }{ m } _{ 2 } }{ { r }^{ 2 } } $
${ F } _{ 2 }=4{ F } _{ 1 }$

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Three particles of masses $2m, m$ and $2m$ are at the vertices $A, B$ and $C$ of an equilateral triangle $ABC$ of side length $'l'$. Then the intensity if gravitational field at the mid point of side $BC$ is:-

  1. $\dfrac{\sqrt{208}}{3} \dfrac{Gm}{l^2}$
  2. $\dfrac{\sqrt{59}}{3} \dfrac{Gm}{l^2}$
  3. $\dfrac{\sqrt{142}}{3} \dfrac{Gm}{l^2}$
  4. $\dfrac{\sqrt{308}}{3} \dfrac{Gm}{l^2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The gravitational field at the midpoint of BC is the vector sum of the fields from the three masses. Using the geometry of the equilateral triangle, the components cancel or add up to the calculated resultant.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

At some planet gravitational acceleration is $1.96m/sec^{ -2 }$. If is safe to jump from a height of 2 m on earth, then what should be the corresponding safe height for jumping on the planet:

  1. 5 m

  2. 2 m

  3. 10 m

  4. 20 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

G on earth=9.8

ratio between earth and planet$=9.8:1.96$
= 5
so the safe height on the planet is 5 time greater than earth because
gravitational pull of that planet is 5 time less than earth
so required height = height on earth $\times$ 5
$2 \times 5$m
=10 m is the safe height on that planet.
Hence,
option $C$ is correct answer.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Potantial (V) at a point in space is given by $v = x^2 + y^2 + z^2$. Gravitational field at a point (x, y, z) is 

  1. $-2 x \hat{i} - 2 y \hat{j} - 2 z \hat{k}$
  2. $2 x \hat{i} + 2 y \hat{j} + 2 z \hat{k}$
  3. $x \hat{i} + y \hat{j} - z \hat{k}$
  4. $-x \hat{i} - y \hat{j} - z \hat{k}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$v=x^2+y^2+z^2$

$E = \dfrac{{ - dv}}{{dx}}$

$E =  - \left[ {2\hat x + 2y\hat j + 2z\hat k} \right]$

$E =  - 2\hat x - 2y\hat j - 2z\hat k$
So, option $A$ is correct.

Multiple choice physics gravitational fields representing a gravitational field gravitational field circular motion and gravitation

Two block of mass $10 kg$ and $20kg$ is separated by a distance $100 km$. What is the gravitational field (F) if $G=6.674 08 \times  10^{-11} m^3 kg^{-1} s^{-2}$?

  1. $13.34 \times 10^{-16} N$
  2. $1.334 \times 10^{-11} N$
  3. $ 1334 \times 10^{-16} N$
  4. $1.334 \times 10^{-18} N$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given : $m _1 = 10kg$  $m _2 = 20 kg$  $r =10^5 m$
Gravitational force between the blocks $F = \dfrac{G m _1 m _2}{r^2}$
$\therefore$ $F = \dfrac{6.67408 \times 10^{-11} \times 10\times 20}{(10^5)^2}$
$\implies$ $1.334 \times 10^{-18} N$