If the gravitational potential is given by $V = (3x + 4y + 12z) \ J/kg$,then the gravitational intensity at the point $(x = 1, y = 0, z = 3)$ is ....... $N \ kg^{-1}$.

The magnitude of the gravitational field at distances $r_1$ and $r_2$ from the center 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 $r_2 < R$):

The gravitational force on a body of mass $1.5 \,kg$ situated at a point is $45 \,N$. The gravitational field intensity at that point is ......... $N/kg$.

Two bodies of mass $100 \ kg$ and $10^4 \ kg$ are lying one meter apart. At what distance from the $100 \ kg$ body will the intensity of the gravitational field be zero?

The gravitational potential versus distance $r$ graph is represented in the figure. The magnitude of the gravitational field intensity is equal to....... $N/kg$.

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