Gravitation

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8}R$ is the distance between the…

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…

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$A$…

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…

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…

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$S.$

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…

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius$R_{e}.$By firing rockets attached to it, its speed is instantaneously increased in the…

Two stars of masses $3\times\,10^{31}\mathrm{kg}$ each, and at distance $2\times\,10^{11}m$ rotate in a plane about their common centre of mass $O.$ A meteorite passes through $O$ moving perpendicular to the…

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is$\vec{L}$. The magnitude of the areal velocity of the planet is :

A body of mass $m$ is projected with velocity $\lambda\,v_{e}$ in vertically upward direction from the surface of the earth into space. It is given that $v_{e}$ is escape velocity and $\lambda\,<1$. If air resistance 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…