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This item has two statements, labeled I and II. From the four alternatives given below, select the one that most accurately describes the relationship between the statements. Statement I: If a mass M is placed at the centre of a cube of edge length a, the total gravitational flux through the cube’s faces is 4πGM. Statement II: For a field produced by a point source, if the field is directed radially and its magnitude varies with distance r as 1/r^2, then the flux through any closed surface depends only on the amount of source enclosed and not on the surface’s size or shape.

1. Statement I is incorrect, while Statement II is correct.
2. Both Statement I and Statement II are correct, and Statement II correctly explains Statement I.
3. Both Statement I and Statement II are correct, but Statement II does not correctly explain Statement I.
4. Statement I is correct, while Statement II is incorrect.

Correct answer: Both Statement I and Statement II are correct, and Statement II correctly explains Statement I.

Solution

Both statements accurately describe principles of gravitational flux and field theory. Statement I correctly calculates the gravitational flux through the cube due to a mass at its center, while Statement II explains that the flux through any closed surface is determined solely by the enclosed mass, aligning with the concept of gravitational fields.

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