Gravitation Questions

A body weighs $48\text{N}$ on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

The radius of Martian orbit around the Sun is about $4$ times the radius of the orbit of Mercury. The Martian year is $687$ Earth days. Then which of the following is the length of $1$ year on Mercury?

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then :

A body projected vertically from the earth reaches a height equal to the earth's radius before returning to the earth. The power exerted by the gravitational force is greatest:

A planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively, then the ratio $v_1/v_2$ is:

A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth's surface, is:

Starting from the centre of the earth having radius $R$, the variation of $g$ (acceleration due to gravity) is shown by:

The ratio of escape velocity at earth $(v_e)$ to the escape velocity at a planet $(v_p)$ whose radius and mean density are twice as that of earth is:

At what height from the surface of earth the gravitation potential and the value of $g$ are $-5.4\times 10^7\text{J/kg}$ and $6.0{\text{m/s}}^2$ respectively? Take the radius of earth as $6400\text{km}$:

A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25\times 10^6\text{m}$ above the surface of earth. If earth’s radius is $6.38\times 10^6\text{m}$ and $g=9.8{\text{ms}}^{-2}$, then the orbital speed of the satellite is:

A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then:

Dependence of intensity of gravitational field ($E$) of earth with distance ($r$) from centre of earth is correctly represented by:

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = $5.98\times 10^{24}\text{kg}$) have to be compressed to be a black hole?

Infinite number of bodies, each of mass $2\text{kg}$ are situated on the x-axis at distances $1\text{m},2\text{m},4\text{m},8\text{m},\dots$, respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:

A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius ($R$) of the earth. The change in potential energy of the body will be:

A spherical planet has a mass $M_p$ and diameter $D_p$. A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to:

A geostationary satellite is orbiting the earth at a height of $5R$ above the surface, $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is:

The height at which the weight of a body becomes $1/16$ th its weight on the surface of earth (radius $R$) is:

If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by:

Which one of the following plots represents the variation of gravitational field ($I$) due to a thin spherical shell of radius $R$ with distance $r$?

Minimum value of $u$ so a particle of mass $m$ does not return to earth (Mass $M$, Radius $R$):

A particle of mass $M$ is at the centre of a spherical shell of mass $M$ and radius $a$. Gravitational potential at distance $a/2$ from centre is:

A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be:

The radii of circular orbits of two satellites $A$ and $B$ of the earth, are $4R$ and $R$, respectively. If the speed of satellite $A$ is $3V$, then the speed of satellite $B$ will be:

The Figure shows elliptical orbit of a planet $m$ about the sun $S$. The shaded area $SCD$ is twice the shaded area $SAB$. If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B$ then:

Two satellites of earth, $S_1$ and $S_2$, are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statements is true?

The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the earth. The escape velocity of a body from this platform is $f{v}_e$, where $v_e$ is its escape velocity from the surface of the earth. The value of $f$ is :

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [$G=\text{gravitational constant}$ and $c=\text{speed of light}$ ]: