Gravitation

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 :

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…

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…

A satellite of mass$M$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $R$ ($R=$ radius of the earth), it ejects a rocket of mass $\frac{M}{10}$ so that…

The mass density of a spherical body is given by $\rho\,\left(r\right)=\frac{k}{r}$ for $r\leq\,R$ and $\rho\,\left(r\right)=0$ for $r>R,$ where $r$ is the distance from the center. The correct graph that describes…

A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its…

When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal, it takes time $T.$When the same body slides down from the rest along a rough inclined plane making the…

The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10R$,where $R$ is the radius of the earth, may be described in termsof escape velocity…

A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac{10^4 R}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g=10…

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion.…

Four spheres each of mass$m$form$a$square of side$d$(as shown in figure). A fifth sphere of mass$M$is situated at the centre of square. The total gravitational potential energy of the system is

If$R_{E}$be the radius of Earth, then the ratio between the acceleration due to gravity at a depth$r$ below and a height$r$ above the earth surface is: (Given :$r<R_{E}$)