Gravitation PYQs

The amount of work done to raise a mass 'm' from the surface of the Earth to a height equal to the radius of the Earth 'R' will be:

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

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?

A body weighs 48 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 mass of a planet is 1/10th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be : (G = gravitational constant)

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G the universal constant of gravitation, the quantity 3π/Gd represents:

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of gravitational field intensity at that point is:

Match List-I with List-II:

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius four times that of Earth and same density is

A particle is released from a height $S$ from the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of Earth and the speed of the particle at that instant are respectively:

A particle of mass m is projected with a velocity v = kVₑ (k < 1) from the surface of the earth, where Vₑ is the escape velocity. The maximum height above the surface reached by the particle is:

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final − initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,

The time period of a geostationary satellite is $24\ \text{h}$, at a height $6R_E$ ($R_E$ is radius of earth) from surface of earth. The time period of another satellite whose height is $2.5R_E$ from surface of earth will be:

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are $K_A$, $K_B$ and $K_C$ respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then:

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following would not be correct?

The acceleration due to gravity at a height $1\ \text{km}$ above the earth is the same as at a depth $d$ below the surface of earth. Then

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

If $\theta_1$ and $\theta_2$ are the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\theta$ is given by:

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

A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. In terms of $g_0$, the value of the total energy 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,

A remote-sensing satellite of Earth revolves in a circular orbit at a height of $0.25\times10^6\,\text{m}$ above the surface of Earth. If Earth's radius is $6.38\times10^6\,\text{m}$ and $g=9.8\,\text{ms}^{-2}$, then the orbital speed of the satellite is:

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?

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

A stone falls freely under gravity. It covers distances $h_1$, $h_2$ and $h_3$ in the first $5\ \text{s}$, the next $5\ \text{s}$ and the next $5\ \text{s}$ respectively. The relation between $h_1$, $h_2$ and $h_3$ is:

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

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

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

Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are respectively M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is:

A particle of mass M is situated at the centre of a spherical shell of mass M and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be:

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2$ ($R_2 > R_1$) is

The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below. The correct figure is

The figure shows the 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:

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 fve, where ve is its escape velocity from the surface of the earth. The value of f is:

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:

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is: