Tag: circular motion and gravitation

Quizzes (5) Questions (66)

Questions Related to circular motion and gravitation

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.
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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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 $({ v } _{ c }=11.2km/sec)$

  1. 12075 K

  2. 10000 K

  3. 20000 K

  4. 10075 K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The escape velocity is related to temperature by the formula v_rms = sqrt(3RT/M). Setting v_rms equal to the escape velocity (11.2 km/s) and solving for T gives approximately 10075 K.

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.