This question contains Statement - 1 and Statement - 2. of the four choices given after the statements, choose the one that best describes the two statements. Statement - 1: For a mass M kept at the center of a cube of side 'a', the flux of gravitational field passing through its sides 4π GM. Statement - 2: If the direction of a field due to a point source is radial and its dependence on the distance 'r' from the source is given as 1/r², its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface. (a) Statement - 1 is false, Statement - 2 is true (b) Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1 (c) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1 (d) Statement - 1 is true, Statement - 2 is false

Answer: (b). Gauss's law for gravity: flux through any closed surface = 4π G Menc (magnitude), for a 1/r² radial field. Statement 2 is true: the flux depends only on the enclosed mass, not on the size or shape of the surface. Statement 1 follows from it: the cube encloses M, so total flux = 4π GM. So the answer is (b).

This question contains Statement - 1 and Statement - 2. of the four… | JEE Main 2008 (AIEEE)

Q16JEE Main 2008 · AIEEEDifficult

Gravitational Field

This question contains Statement - $1$ and Statement - $2$ . of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $1$ :

For a mass $M$ kept at the center of a cube of side $'a'$ , the flux of gravitational field passing through its sides $4\pi GM.$

Statement - 2:

If the direction of a field due to a point source is radial and its dependence on the distance $'r'$ from the source is given as $\frac{1}{r^2},$ its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

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Answer: (b)

Gauss's law for gravity: flux through any closed surface $= 4\pi G M_{enc}$ (magnitude), for a $\frac{1}{r^2}$ radial field.
Statement 2 is true: the flux depends only on the enclosed mass, not on the size or shape of the surface.
Statement 1 follows from it: the cube encloses $M$ , so total flux $= 4\pi GM$ .
So the answer is (b).

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