A thin rod of length $L$ is bent to form a semicircle. The mass of rod is $M.$ What will be the gravitational potential at the centre of the circle?
$-\frac {GM}{L}$
$ - \frac{{GM}}{{2\pi L}}$
$ - \frac{{\pi GM}}{{2L}}$
$ - \frac{{\pi GM}}{{L}}$
A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, is velocity must be increased ........ $\%$
A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is
A body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is
where $g$ is acceleration due to gravity at the surface of earth.
Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r\geq $ radius of the planet. Plots $1$ and $2$ coincide for $r\geq R_2$ and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is