Gravitation

Consider two solid spheres of radii $R_{1}=1m$,$R_{2}=2m$ and masses $M_{1}$ and $M_{2},$ respectively. The gravitational field due to sphere $\left(1\right)$ and $\left(2\right)$ are shown. The value of…

From a solid sphere of mass $M$ and radius $R\text{,}$ a spherical portion of radius $\left(\frac{R}{2}\right)$ is removed as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty\,,$ the potential at…

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is…

The figure shows an elliptical path $ABCD$ of a planet around the sun $S$ such that the area of triangle $CSA$ is $\frac{1}{4}$ the area of the ellipse. (see figure) with $DB$ as the major axis, and $CA$ as the minor…

Two satellites$A$ and$B$of masses $200\mathrm{kg}$ and $400\mathrm{kg}$ are revolving round the earth at height of $600\mathrm{km}$ and $1600\mathrm{km}$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of$A$…

The mass density of a spherical galaxy varies as$\frac{K}{r}$over a large distance$r$from its center. In that region, a small star is in a circular orbit of radius$R$. Then the period of revolution,$T$depends on$R$as:

A solid sphere of radius $R$ gravitationally attracts a particle placed at $3R$ from its centre with a force $F_{1}.$ Now a spherical cavity of radius $\left(\frac{R}{2}\right)$ is made in the sphere (as shown in…

In the reported figure of earth, the value of acceleration due to gravity is same at point$A$ and $C$but it is smaller than that of its value at point$B$ (surface of the earth). The value of $OA:AB$will be $x:5$. The…

India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at $E$ and meets Mars at $M$. If the semi-major axis of Earth's orbit 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:

Suppose two planets (spherical in shape) of radii $R$ and $2R,$but mass $M$ and $9M$ respectively have a centre to centre separation $8R$ as shown in the figure. A satellite of mass $m$is projected from the surface of…

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is$S.$