$A$ mass $m$ is placed at point $P$ on the axis of a ring of mass $M$ and radius $R$ at a distance $R$ from its centre. The gravitational force on mass $m$ is

$A$ 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 ..... $N/kg$.

$A$ metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

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

$A$ 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 $h = r$?

An infinite number of masses,each of $1 \ kg$,are placed on the $+ve \ X$-axis at $1 \ m, 2 \ m, 4 \ m, \dots$ from the origin. The magnitude of the gravitational field at the origin due to this distribution of masses is: