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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&nbsp;<span>where</span>&nbsp;any other body that has mass will experience a force of repulsion.

  3. A gravitational field is a region&nbsp;<span>where</span>&nbsp;any other body that has mass will experience no force of attraction.

  4. A gravitational field is a region&nbsp;<span>where</span>&nbsp;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

A gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. 

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
  • The gravitational field is the actually the force experimented by a unit mass due to a body of mass M.
  • So when a unit mass is kept at a distance 'r' from mass 'M' then it experiences a force which is equal to $\dfrac{GM}{r^2}$[as m=1],which is nothing but the gravitational field of mass M.
  • Its units are $\dfrac{N}{kg}$
  • Hence the above statement is true.