Tag: circular motion and gravitation

Questions Related to 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:

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

  1. Zero

  2. $\frac{3GM}{L^2}$

  3. $\frac{9GM}{L^2}$

  4. $\frac{12}{\sqrt{3}}\frac{GM}{L^2}$

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Correct Option: A
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 $zero.$

The gravitational field lines are

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

  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

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Correct Option: A
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

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

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

  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

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Correct Option: B
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)

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,

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

  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

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Correct Option: A
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)

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

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

  1. Infinitely many

  2. Zero

  3. Varying number depending upon surface area

  4. Varying number depending upon volume

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Correct Option: B
Explanation:

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