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 ............

Infinite number of masses each of $3 \ kg$ are placed along a straight line at the distances of $1 \ m, 2 \ m, 4 \ m, 8 \ m, \ldots$ from a point $O$ on the same line. If $G$ is the universal gravitational constant,then the magnitude of gravitational field intensity at $O$ is (in $G$)

The gravitational intensity at the centre $O$ of a hemispherical shell of uniform mass density has the direction indicated by which arrow?

Find the gravitational force of attraction between the ring and the sphere as shown in the diagram. The plane of the ring is perpendicular to the line joining the centres. The distance between the centres of the ring (mass $m$) and the sphere (mass $M$) is $\sqrt{8}R$,where both have an equal radius $R$.

What is the intensity of the gravitational field at the center of a spherical shell?

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