Which one of the following graphs correctly represents the variation of the gravitational field $(I)$ with the distance $(r)$ from the centre of a spherical shell of mass $M$ and radius $a$?

  • A
    Option A
  • B
    Option B
  • C
    Option C
  • D
    Option D

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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 centre of a cube of side '$a$',the flux of the gravitational field passing through its sides is $-4\pi GM$.
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.

$A$ thin rod of length $L$ is bent in the form of a circle. Its mass is $M$. What force will act on a mass $m$ placed at the centre of this circle? $(G = \text{universal gravitational constant})$

If a cavity is made inside a solid sphere,then the gravitational field inside the cavity is

$A$ mass $m$ is placed at $P$ at a distance $h$ along the normal through the centre $O$ of a thin circular ring of mass $M$ and radius $r$. If the mass is moved further away such that $OP$ becomes $2h$,by what factor will the force of gravitation decrease,if $h = r$?

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The gravitational field in a region is given by $\vec{E} = (5\,N/kg)\,\hat{i} + (12\,N/kg)\,\hat{j}$. If the potential at the origin is taken to be zero,then the ratio of the potential at the points $(12\,m, 0)$ and $(0, 5\,m)$ is:

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