For the given hemispherical shell,the direction of the gravitational intensity at an arbitrary point $P$ on its rim is indicated by which arrow?

Two point masses having mass $m$ and $2m$ are placed at a distance $d$. The point on the line joining the point masses,where the gravitational field intensity is zero,will be at a distance ............

The mass density inside a solid sphere of radius $R$ varies as $\rho(r)=\rho_0\left(\frac{r}{R}\right)^\beta$,where $\rho_0$ and $\beta$ are constants and $r$ is the distance from the centre. Let $E_1$ and $E_2$ be gravitational fields due to the sphere at distances $\frac{R}{2}$ and $2R$ from the centre of the sphere,respectively. If $\frac{E_2}{E_1}=4$,the value of $\beta$ is

The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho(r) = \rho_{0} \left(1 - \frac{r^{2}}{R^{2}}\right)$. Then the gravitational field is maximum at:

$A$ spherical shell is cut into two pieces along a chord as shown in the figure. $P$ is a point on the plane of the chord. The magnitude of the gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

The figure shows a hemispherical shell. The direction of the gravitational field intensity at point $p$ will be along