Gravitation

The time period of Earth is 1 year at a distance of 1 AU. What would be the period of a planet at a distance of 0.25 AU?

In the elliptical path of a planet, what are the two fixed points that define the ellipse called?

If the distance from the Sun $R$ becomes 9 times greater, by what factor does the orbital period $T$ increase?

Which of the following is true regarding the orbital periods of planets in the Solar System?

According to Kepler's third law, the ratio $T^2/R^3$ is a constant. The value of this constant is approximately $3 \times 10^{-19} s^2/m^3$ for the Sun. For a different star with twice the mass of the Sun, this constant would be:

If the mass of a planet is doubled while keeping its orbital radius the same, its period of revolution will:

The distance of a planet from the Sun at perihelion is $0.5$ AU and at aphelion is $1.5$ AU. What is the semi-major axis of its orbit?

The time period $T$ of a satellite in a circular orbit of radius $R$ is $T$. If it is to be put into an elliptical orbit such that its maximum distance from the planet's center is $R$ and minimum distance is $R/3$, what will be its new time period?

For an elliptical orbit with eccentricity $e$, the ratio of the velocity at the end of the minor axis to the velocity at the perihelion is:

What is the ratio of the kinetic energy to the total mechanical energy for a satellite in a circular orbit?

According to the Universal Law of Gravitation, the force $F$ between two point masses $m_1$ and $m_2$ separated by a distance $r$ is given by the formula $F = G \frac{m_1 m_2}{r^2}$. Based on this relationship, what is the dimensional formula for the Universal Gravitational Constant ($G$)?

If a body of mass $m$ is moved from the Earth's surface to a height equal to the Earth's radius, the distance from the Earth's center is doubled. The force of gravity on the body becomes:

If the mass of the Earth were to double without any change in its size, the gravitational force it exerts on an object on its surface would:

The universal gravitational constant $G$ does NOT depend on:

Two stationary point masses $A$ and $B$, with masses $m$ and $9m$ respectively, are fixed at a distance $r$ from each other. A third point mass $C$ is placed exactly at the midpoint of the line segment joining $A$ and $B$. What is the ratio of the magnitude of the gravitational force exerted by mass $A$ on $C$ to the magnitude of the net gravitational force acting on mass $C$?

Three identical point masses, each of mass $M$, are positioned at the vertices of a right-angled isosceles triangle. Mass B is located at the vertex containing the $90^{\circ}$ angle, while masses A and C are at the other two vertices such that $AB = BC = L$. What is the magnitude of the net gravitational force acting on mass B due to the other two masses?

According to Newton's law of gravitation, the force between two point masses is inversely proportional to the square of the distance between them. This is an example of:

A satellite is orbiting Earth at an altitude $h = R$ (where $R$ is Earth's radius). The gravitational force on the satellite is $F$. If the satellite moves to an altitude $h = 2R$, the new force is:

If the Earth were to stop rotating, the value of $g$ at the equator would:

A point mass $m$ is placed at $(R, 0)$ and another mass $2m$ is placed at $(0, R)$. What is the magnitude of the gravitational force on a mass $M$ placed at the origin $(0,0)$?

If an object is moved from the Earth's surface to a deep mine, its weight will:

The value of $g$ used for standard gravity calculations is exactly:

What is the ratio of $g$ at height $h = R/2$ to $g$ at the surface?

The value of $g$ is minimum at which latitude?

If the Earth's angular velocity is increased to $17$ times its current value, the acceleration due to gravity at the equator will become:

If $R$ is the radius of Earth, the height at which the acceleration due to gravity becomes $g/9$ is $h_1$ and the depth at which it becomes $g/9$ is $d_1$. The ratio $h_1/d_1$ is:

The weight of a body at the center of the Earth is:

The decrease in the value of $g$ at a height $h$ is $\Delta g_1$ and at a depth $d$ is $\Delta g_2$. If $h = d = R/10$, then:

If $g_1$ is the acceleration due to gravity at a height $h = R$ and $g_2$ is the acceleration at a depth $d = R$, then the ratio $g_1 / g_2$ is:

At what latitude is the apparent value of $g$ equal to $g - \frac{1}{4}\omega^2 R$?

Which of the following is a characteristic of a conservative force like gravity?

Two bodies of masses $M$ and $m$ are placed $r$ distance apart. If $m$ is moved slightly closer to $M$, the potential energy:

Potential energy is zero when the distance $r$ is:

If the gravitational potential energy of an object is $-100 J$, what is the minimum work required to remove it completely from the gravitational field?

A particle of mass $m$ is projected vertically upwards from the surface of Earth with a kinetic energy equal to half of the minimum energy required to escape. The maximum height attained by the particle is:

The work done in shifting a unit mass from the center of Earth to the surface of Earth is:

If the gravitational potential on the surface of Earth is $V_0$, then the potential at a point $P$ at height $h = R$ is $V_P$. The value of $V_P$ is:

Three particles of mass $m$ are placed on a straight line such that the distance between adjacent particles is $d$. What is the total gravitational potential energy of this system?

A particle of mass $m$ is placed at the center of a uniform spherical shell of mass $M$ and radius $R$. What is the gravitational potential energy of the system?

What is the escape velocity from the center of a uniform solid sphere of mass $M$ and radius $R$?

Escape velocity is a property that characterizes:

If the escape velocity from Earth is $11.2$ km/s, what is the escape velocity from a planet with the same radius but $1/4$ the mass of Earth?

The work done in shifting a body of mass $m$ from the surface of Earth to infinity is:

A body is projected with a speed $v = 1.5 v_e$. The body will:

A narrow, frictionless tunnel is bored through the center of a uniform solid spherical planet of mass $M$ and radius $R$. If $v_e$ is the escape velocity for an object launched from the surface of the planet, what is the minimum velocity required to project a particle from the center of the planet through the tunnel so that it escapes to infinity?

Which of the following graphs best represents the variation of escape velocity $v_e$ with the mass $m$ of the object being projected?

If the escape velocity on Earth is $11.2\text{ km/s}$ and $g = 9.8\text{ m/s}^2$, what is the radius of Earth used in this calculation?

Two identical planets, each of mass $M$ and radius $R$, are fixed in space such that the distance between their centers is $10R$. A projectile is launched from the 'outer pole' of one planet (the point on its surface furthest from the second planet) along the line joining the centers. What is the escape velocity required for the projectile to reach infinity?

A hypothetical planet of radius $R$ has a non-uniform mass density $\rho(r) = k r$, where $k$ is a constant and $r$ is the distance from the center. If the escape velocity from the surface of this planet is $v_s$, what is the escape velocity of a particle launched from the center of the planet through a narrow, radial, frictionless tunnel?

A planet of mass $M$ and radius $R$ is surrounded by a concentric, thin uniform spherical shell of the same mass $M$ and radius $3R$. A small particle is located on the surface of the planet. What is the minimum velocity required for this particle to escape the combined gravitational field of the planet and the shell to infinity?

The orbital velocity of a satellite is independent of:

For a satellite in a circular orbit, the centripetal acceleration is provided by:

Which law of physics explains the dependency of orbital period on the orbital radius (linked to orbital velocity)?

What happens to the orbital velocity of a satellite if the radius of its orbit is decreased?

A satellite is orbiting around Earth. What happens to its orbital velocity if the orbital radius is doubled and the mass of the planet it orbits is also doubled?

If a planet has mass $M$ and radius $R$, the orbital speed of a satellite orbiting at a height $h = R/3$ is:

For a satellite to be in a stable circular orbit, the centripetal force must be provided by:

For a satellite in circular orbit, the centripetal acceleration $a_c$ is related to the orbital velocity $v$ and radius $r$ as $a_c = v^2/r$. If the orbital velocity is expressed in terms of $g$ (surface gravity) and $R$ (planet radius) for a height $h$, then $a_c$ is:

A satellite revolves around a planet in a circular orbit. If the mass of the planet is quadrupled and the orbital radius is doubled, the orbital velocity becomes:

What is the work done by the gravitational force on a satellite of mass $m$ moving in a circular orbit of radius $r$ with orbital velocity $v$ during half a revolution?