Gravitation — JEE Main PYQs

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in 24 hours around the plane?
[Given: Mass of plane …

A satellite is revolving in a circular orbit at a height h from the earth surface, such that $\mathrm{h}\ll \mathrm{R}$ where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the sa …

A straight rod of length $L$ extends from $x=a$ to $x=L+a$. The gravitational force it exerts on a point mass '$m$' at $x=0$, if the mass per unit length of the rod is $A+B{x}^2$, is given by:

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collis …

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9:4$. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If ' $R$ ' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same ma …

Two satellites, $A$ and $B$, have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, $T_A/T_B$, is :

A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho (r)=\frac{K}{r^2}$. Identify the correct relation between the radius $R$ of the particle's orbit and its period T:

The energy required to take a satellite to a height ' $h$ ' above Earth surface (radius of Earth $=6.4\times 10^3\mathrm{km}$) is ${\mathrm{E}}_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is ${\mathrm{E}}_2$. The value of …

The value of acceleration due to gravity at Earth's surface is $9.8{\mathrm{ms}}^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9{\mathrm{ms}}^{-2}$, is close to: (Radius of earth $=6.4\times 10^6\mathrm{m}$)

A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the ${\mathrm{n}}^{\text{th }}$ power of $R$. If the period of rotation of the particle is T , then :

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R=$ Earth's radius):

A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth $R$; $h\ll R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect …

From a solid sphere of mass M and radius R , a spherical portion of radius $\mathrm{R}/2$ is removed, as shown in the figure. Taking gravitational potential $\mathrm{V}=0$ at $\mathrm{r}=\infty$, the potential at the centre of the cavity thus formed is ( $\mathrm{G}=$ gravitati …

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2 R ?

The mass of a spaceship is 1000 kg . It is to be launched from the earth's surface out into free space. The value of ' $g$ ' and ' $R$ ' (radius of earth) are $10\mathrm{m}/{\mathrm{s}}^2$ and 6400km respectively. The required energy for this work will be ;

Two bodies of masses m and 4 m are placed at a distance r . The gravitational potential at a point on the line joining them where the gravitational field is zero is:

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g=$ the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth is

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11{\mathrm{kms}}^{-1}$, the escape velocity from the surface of the planet would be

Average density of the earth

The change in the value of $g$ at a height ' $h$ ' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both 'd' and ' $h$ ' are much smaller than the radius of earth, then which one of the following is correct?

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take …

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

The time period of an earth satellite in circular orbit is independent of

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius $R$ around the sun will be proportional to