Tag: circular motion and gravitation

Questions Related to 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 

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

  1. $\dfrac{k}{x}$

  2. $\dfrac{k}{2x^2}$

  3. $\dfrac{k}{x^4}$

  4. $\dfrac{k}{x^6}$

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Correct Option: B
Explanation:

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

The gravitational intensity is denoted by :

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

  1. $g$

  2. $G$

  3. $E$

  4. none of these

Show answer
Correct Option: A
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.

A gravitational field is

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

  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

Show answer
Correct Option: C
Explanation:

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

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. 

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

  1. True

  2. False

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Correct Option: A
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.

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

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

  1. Halved

  2. Quadrupled

  3. Doubled

  4. Reduced to a quarter

Show answer
Correct Option: B
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 } } $
${ F } _{ 2 }=4{ F } _{ 1 }$

Under the force of gravity, a heavy body falls quicker than a light body (neglect air resistance).

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

According to newton's laws the time taken to fall is not related to mass

$S=ut+\dfrac { 1 }{ 2 } { at }^{ 2 }$
${ V }^{ 2 }-{ u }^{ 2 }=2as$
It have not to do anything with mass so both lighter and heavier body will taken same time to fall from certain point.

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:-

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

  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. $\dfrac{\sqrt{308}}{3} \dfrac{Gm}{l^2}$

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Correct Option: A

PRESSURE AND KINETIC INTERPRETATION OF TEMPERATURE
At what temperature the mean kinetic energy of hydrogen molecules increases to such that they will escape out of the gravitational field of earth for over?
take $({ v } _{ c }=11.2km/sec)$

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

  1. 12075 K

  2. 10000 K

  3. 20000 K

  4. 10075 K

Show answer
Correct Option: D

The gravitational field in a region is given by $\vec {g} = 2\hat {i} + 3\hat {j} m/s^{2}$. The work done in moving a particle of mass $1\ kg$ from $(1, 1)$ to $\left (2, \dfrac {1}{3}\right )$ along the time $3y + 2x = 5$ is

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

  1. Zero

  2. $20\ J$

  3. $-15\ J$

  4. $18\ J$

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Correct Option: C

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:

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

  1. 5 m

  2. 2 m

  3. 10 m

  4. 20 m

Show answer
Correct Option: C
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.