Gravitational Field

The magnitude of gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius R and mass M are $I_1$ and $I_2$ respectively. Given that $r_1 >$ $R$ and $r_2 <$ $R$, the ratio $\frac{I_1}{I_2}$ is

The magnitude of gravitational field at distance $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $E_1$ and $E_2$ respectively. If $r_1 > R$ and $r_2 < R$, then the ratio $E_1/E_2$ is

A uniform sphere has radius ' $R$ ' and mass ' $M$ '. The magnitude of gravitational field at distances ' $r_1$ ' and ' $r_2$ ' from the centre of the sphere are ' $E_1$ ' and ' $E_2$ ' respectively. The ratio $E_1 : E_2$ is ($r_1 > R$ and $r_2 < R$)

A uniform solid sphere of mass ' $m$ ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' $2r$ ' and mass ' $m$ ' then the gravitational field

The magnitude of gravitational field at distance ' $r_1$ ' and ' $r_2$ ' from the centre of a uniform sphere of radius ' $R$ ' and mass ' $M$ ' are ' $F_1$ ' and ' $F_2$ ' respectively. The ratio ' $(F_1/F_2)$ ' will be (if $r_1 > R$ and $r_2 < R$)

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

In a gravitational field, the gravitational potential is given by, $V = -\frac{K}{x}$ (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

The mass of earth is 81 times the mass of the moon and the distance between their centres is $R$. The distance from the centre of the earth, where gravitational force will be zero is

Consider two solid spheres of radii R1 = 1m, R2 = 2m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M_1}{M_2}$ is:

The mass density of a planet of radius R varies with the distance r from its centre as $\rho$(r) = $\rho_0 (1$ $- \frac{r^2}{R^2})$.

Then the gravitational field is maximum at:

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be:

The mass density of a spherical body is given by

$\rho$ (r) = $\frac{k}{r}$ for r $\le$ R and $\rho$ (r) = 0 for r > R,

where r is the distance from the centre.

The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is:

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly):

Which one of the following plots represents the variation of gravitiational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

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.