Tag: representing a gravitational field

Questions Related to representing a gravitational 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.