Directions : The following question contains statemen-1 and statement -2  of the four choices   given, choose the one that best describes the two statements.statemen-1  For a mass  M kept at the centre of a cube of side  a  The flux of gravitational field  passing through its sides                     is       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 , 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    Option 1) statemen-1 is true ,and statement -2 false . Option 2) statemen-1 is false ,and statement -2 true . Option 3) statement-1 is true ,and statement -2 true  ;         statement -2 is a correct explanation for statement -1 Option 4) statemen-1 is true ,and statement -2 true  ;         statement -2 is not a correct explanation for statement -1

As we learnt in

$\dpi{100} Let A \; be \; the \; Gaussian\; surface\; enclosing \; a$ $\dpi{100} spherical \; charge\; Q$

$\dpi{100} \vec{E}.4\pi r^{2}=\frac{Q}{\varepsilon _{0}}$

$\dpi{100} \vec{E}=\frac{Q}{4\pi \varepsilon _{0}.r^{2}}$

$\dpi{100} Flux\; \phi =\vec{E}.4\pi r^{2}=\frac{Q}{\varepsilon _{0}}$

Every line passing through $\dpi{100} A$ has to pass through $\dpi{100} B$, whether $\dpi{100} B$ is a cube or any surface. It is only for Gaussian surface, the lines of field should be normal. Assuming the mass is a point mass. $\dpi{100} \vec{g}$ , $\dpi{100} gravitational \; field =-\frac{GM}{r^{2}}$

$\dpi{100} Flux\; \phi _{g}=\left | \vec{g}.4\pi r^{2} \right |=\frac{4\pi r^{2}.GM}{r^{2}}=4\pi GM.$

Here $\dpi{100} B$ s a cube. As explained earlier, whatever be the shape, all the lines passing through $\dpi{100} A$ are passing through $\dpi{100} B$, although all the lines are not normal.

Statement­ 2 is correct because when the shape of the earth is spherical, area of the Gaussian surface is $\dpi{100} 4\pi r^{2}$. This ensures inverse square law.

Let A be the Guassion surface enclosing a sperical charge Q.

Everyline passing through A has pass through B, whether B is a cube or any surface, it is only for guassion surface, the lines of fixed should be normal, Assuming the mass is a point mass.

thus

Here B is a cube. As explained earlier, whatever be the shape, all the lines passing through A are passing through B. Although all the lines are not normal.

Statement 2 is covered because when the shape of the earth is spherical, area of the gaussian surface is

Option 1)

statemen-1 is true ,and statement -2 false .

Incorrect option

Option 2)

statemen-1 is false ,and statement -2 true .

Incorrect option

Option 3)

statement-1 is true ,and statement -2 true  ;

statement -2 is a correct explanation for statement -1

Correct option

Option 4)

statemen-1 is true ,and statement -2 true  ;

statement -2 is not a correct explanation for statement -1

Incorrect option