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.

Gravitational fieldCenter of massPlanetary densityHill SphereSpace-time curvature

Gravitation and Center of Mass Questions

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

If the radius of the earth were to shrink and its mass were to remain the same, the acceleration due to gravity on the surface of the earth with?

  1. Increase

  2. Decrease

  3. Remains same

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

Gravitational force between two masses = $\quad K\dfrac { m1m2 }{ { r }^{ 2 } } \quad \quad $

Where

K is universal gravitational constant $m _1$ and $m _2$ are the masses $r$ is the distance between the masses.

Now , the acceleration due to $ m1 $ being earth will be = $ K\dfrac { m1 }{ { r }^{ 2 } } \quad \quad $

If the radius decreases and the mass remains same the acceleration will increase.

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

What is the gravitational field strength at the surface of Jupiter (mass $1.9\times 10^{27} kg$, radius $7.1\times 10^7 m$?

  1. $25 N kg^{-1}$
  2. $25 N kg^{-2}$
  3. $35 N kg^{-1}$
  4. $55 N kg^{-2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravitational field = $ K\dfrac { m1 }{ { r }^{ 2 } } \quad $

where $K$ is universal gravitational constant $m _1$ is the mass $r$ is the distance. 

G= $ 6.67\times { 10 }^{ -11 }\dfrac { 1.9({ 10 }^{ 27 }) }{ { (7.1\times { 10 }^{ 7 }) }^{ 2 } } \quad \quad $ 

   =  $\quad 25N{ kg }^{ -1 }\quad $

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

Three particles each of mass m are kept at verticles of an equilateral triangle of side L. The gravitational field at centre due to these particle is:

  1. Zero
  2. $\frac{3GM}{L^2}$
  3. $\frac{9GM}{L^2}$
  4. $\frac{12}{\sqrt{3}}\frac{GM}{L^2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that for an equilateral triangle the line joining the center of gravity to each vertex of the triangle are each at angle $120^0$ and we also know that the field by each mass will be along these lines joining the center and vertex.

Also as the triangle is equilateral so all the vertex will be at same distance from the center, so the filed produced by each mass will be same.
Now as the field produced are eqaul in magnitude and at angle $120^0$ so 
net field will be $zero.$

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

The gravitational field lines are

  1. Directed inwards towards a particle

  2. Directed outwards from a particle

  3. Directed along the particle's motion

  4. Directed perpendicular to the particle's motion
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The gravitational field lines are directed inwards towards a particle because at any point on the earth's field, a body will feel a force directed towards the center of the earth. The field lines becomes more spread out as the distance form the earth increases, which indicates the diminishing strength of the field

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

Two masses m and  100m are kept at points A and B. The gravitational field lines

  1. Will be crowded at A than B

  2. Will be crowded at B than A

  3. Will be crowded equally at A and B

  4. Diverge from both the masses
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The strength of a gravitational field is given by the number of lines crowding at a point. This field strength is given by $GM/R^2$. Thus, it is proportional to the mass of the object

Larger the mass, more the field intensity and hence the number of lines of forces

Thus, the correct option is (b)

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

The field strength for a planet A of mass M and radius R is F. In another planet, the density is found to be 27 times the density of the planet A and the radius of the new planet is one third of A. Then,

  1. Number of lines of force in both A and B are same

  2. Number of lines of force in A is more than B

  3. Number of lines of force in B is more than A

  4. Number of lines of force cannot be determined with this information
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Number of lines of force is given by the flux $\phi=\int (g.dA)=(GM/R^2)4 \pi R^2 = 4 \pi GM$

Thus, number of lines of forces is proportional to M. 

So, $M _A= \rho (4 \pi R^3)/3$ AND $M _B=27 \rho (4 \pi [R/3]^3)/3=\rho (4 \pi R^3)/3$

The mass of both the planets are same AND hence the flux is also same for both the planets

The correct option is (a)

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

There are _____ gravitational lines of force inside a spherically symmetric shell

  1. Infinitely many

  2. Zero

  3. Varying number depending upon surface area

  4. Varying number depending upon volume
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As there is no gravitational field in the shell, there are zero gravitational lines of force inside a spherically symmetric shell.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Find the radiation pressure of solar radiation on the surface of earth. Solar constant is $1.4kW{{m}^{-2}}$

  1. $4.7\times { 10 }^{ -5 }Pa$
  2. $4.7\times { 10 }^{ -6 }Pa$
  3. $2.37\times { 10 }^{ -6 }Pa$
  4. $9.4\times { 10 }^{ -6 }Pa$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
METHOD-1:
${Pressure} _{absorbed}=\dfrac{E _{f}}{c}$
${E} _{f}=$ energy flux, $C=$ Speed of light

${ Pressure } _{ absorbed }=\dfrac { 1.4\times 1000 }{ 3\times { 10 }^{ 8 } } =4.66\times { 10 }^{ -6 }Pa$

METHOD-2: (checking the unit,if formula is not remembered)

We know that:
${Power}={force}\times{velocity}$-----(1)
${Pressure}=\dfrac{force}{area}$------(2)

${Force}=\dfrac{power}{velocity}=\dfrac { 1.4\times 1000 }{ 3\times { 10 }^{ 8 } } =4.66\times { 10 }^{ -6 } newton$

Put in equation (2)
${ Pressure } _{ absorbed }=\dfrac { 4.66\times { 10 }^{ -6 }N }{ { m }^{ 2 } } =4.66\times { 10 }^{ -6 }Pa$
Multiple choice

The principle of conservation of mass states that:

  1. Mass can be created or destroyed.

  2. Mass can be transferred from one place to another.

  3. Mass remains constant in a closed system.

  4. Mass is proportional to volume.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The principle of conservation of mass states that mass can neither be created nor destroyed, only transferred from one place to another.

Multiple choice

What factors determine the Roche Limit?

  1. The masses of the two celestial bodies.

  2. The densities of the two celestial bodies.

  3. The distance between the two celestial bodies.

  4. All of the above.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Roche Limit is determined by the masses, densities, and distance between the two celestial bodies. The more massive the larger body, the denser the smaller body, and the closer the two bodies are, the smaller the Roche Limit will be.

Multiple choice

What is the mathematical formula for calculating the force of gravity between two objects?

  1. $$F = Gm_1m_2/r^2$$
  2. $$F = ma$$
  3. $$F = kx$$
  4. $$F = q_1q_2/r^2$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This formula is known as Newton's law of universal gravitation.

Multiple choice

What is the relationship between gravity and the geoid?

  1. Gravity causes the geoid to bulge at the equator

  2. Gravity causes the geoid to be flattened at the poles

  3. Gravity causes the geoid to be a perfect sphere

  4. Gravity has no effect on the geoid
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravity causes the Earth's mass to be concentrated at the center, which in turn causes the geoid to bulge at the equator. This is because the force of gravity is stronger at the poles than at the equator.

Multiple choice

What is the role of gravity in determining the Earth's shape?

  1. Gravity pulls the Earth's mass towards the center, causing it to be spherical

  2. Gravity causes the Earth to rotate, which flattens it at the poles

  3. Gravity causes the Earth to bulge at the equator

  4. Gravity has no effect on the Earth's shape
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravity is the force that pulls the Earth's mass towards the center, causing it to be spherical. The Earth's rotation also contributes to its shape, causing it to be flattened at the poles and bulge at the equator.

Multiple choice

What is the role of gravity in the formation of the Earth's core?

  1. Gravity pulls the Earth's material towards the center, causing the core to form

  2. Gravity pushes the Earth's material away from the center, causing the core to form

  3. Gravity has no effect on the formation of the Earth's core

  4. Gravity causes the Earth's material to rotate, causing the core to form
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravity pulls the Earth's material towards the center, causing the core to form. This process is known as accretion.

Multiple choice

What is the role of gravity in the formation of the Earth's moon?

  1. Gravity pulls the Earth's material towards the center, causing the moon to form

  2. Gravity pushes the Earth's material away from the center, causing the moon to form

  3. Gravity has no effect on the formation of the Earth's moon

  4. Gravity causes the Earth's material to rotate, causing the moon to form
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravity pulls the Earth's material towards the center, causing the moon to form. This process is known as accretion.