Gravitation

Newton's derivation of the inverse square law of gravity was based on which of Kepler's laws?

The Harmonic Law is another name for:

What is the eccentricity of a perfectly circular orbit?

If a planet's orbit is a circle of radius $r$, then $T^2$ is proportional to:

A planet of mass $m$ moves in an elliptical orbit. If $r_{max}$ and $r_{min}$ are the maximum and minimum distances from the sun, the semi-major axis $a$ is:

Two planets $A$ and $B$ orbit a star. The orbital radius of $A$ is $R$ and that of $B$ is $16R$. What is the ratio of their periods $T_A / T_B$?

If a planet's orbit is a circle of radius $r$, the area swept by the radius vector in one full period $T$ is $\pi r^2$. The areolar velocity is:

A spacecraft is in a circular orbit around a planet. To put the spacecraft into an elliptical orbit with the same perigee but a higher apogee, the spacecraft must:

A planet revolves around the sun in an elliptical orbit of eccentricity $e$. If $T$ is the period, the time taken by the planet to move from perihelion to the end of the minor axis is:

If the semi-major axis of Earth's orbit is $a$ and its eccentricity is $e$, what is the distance from the Sun to the Earth when it is at the end of the semi-minor axis?

The range of gravitational force is:

Which of the following statements about gravitational force is FALSE?

If the product of two masses is doubled, the gravitational force between them:

The force of attraction between two apples on a table is not noticeable because:

Three identical point masses, each of mass $M$, are placed at the vertices $A, B,$ and $C$ of an isosceles right-angled triangle. The right angle is located at vertex $B$, and the length of the sides $AB$ and $BC$ is $L$. What is the magnitude of the net gravitational force acting on the mass at vertex $B$ due to the other two masses?

If the radius of Earth's orbit is made $1/4$ times its current value, the gravitational force between the Sun and Earth will become:

The force of attraction between two masses is $F$. If the mass of both objects is halved and the distance between them is also halved, then the new force will be:

For a system of two masses $M$ and $m$ in a circular orbit about their center of mass, the orbital period $T$ is given by $T^2 = \frac{4\pi^2 d^3}{G(M+m)}$, where $d$ is the separation. If $M = m$, the speed of each mass is:

The force of attraction between a hollow spherical shell of mass $M$ and a point mass $m$ placed at a distance $d$ from the center ($d > R$) is $F$. If the shell is replaced by a solid sphere of the same mass and radius, the force $F$ will:

If the earth stops rotating, the value of $g$ at the equator will increase by $a \omega^2$. What is the value of $a$?

Which of the following describes the change in $g$ as one goes from the surface to the center?

If we represent the distance from the center of Earth as $r$, then for $r < R$, $g$ is proportional to:

The value of $g$ at the surface of Earth is $9.8 \, m/s^2$. If the Earth's mass is doubled and its radius is doubled, the new value of $g$ will be:

At what height $h$ above the surface is $g_h = g/100$?

At what height $h$ is the value of $g$ equal to $g/100$? (Assume $R = 6400\text{ km}$)

The ratio of the acceleration due to gravity at a depth $R/2$ to the acceleration due to gravity at a height $R/2$ is:

A physical balance measures $10\text{ kg}$ on the surface. If it is taken to a height $h=R$, the mass measured will be:

A density-profile planet has $\rho(r) = \rho_0 r/R$. What is the ratio of $g$ at $r=R/2$ to $g$ at $r=R$?

Find the ratio of the acceleration due to gravity at a height $R/n$ and depth $R/n$ for $n > 1$.

Two equal masses $m$ are placed at a distance $d = R$ and $d = 2R$ from the center of Earth ($R$ is radius). The ratio of the gravitational forces acting on them is:

If a rock is dropped into a deep well, its gravitational potential energy ________ as it falls.

Gravitational potential energy is zero when the distance $r$ is:

If a body of mass $m$ is at the center of a hollow spherical shell of mass $M$ and radius $R$, its gravitational potential energy relative to infinity is:

In a conservative field, like a gravitational field, the round-trip work done is:

If the gravitational potential energy of a particle is $U = -k/r^n$, what is the expression for the gravitational force acting on it?

Two planets have masses $M$ and $16M$ and their centers are separated by distance $D$. The gravitational potential at a point on the line joining their centers where the gravitational field is zero is:

What is the gravitational potential energy of a system of three particles of mass $m$ placed at the corners of a right-angled triangle with sides $a$ and $b$?

At what height $h$ from the surface of Earth is the gravitational potential $1/4$ of its value at the surface?

A point mass $m$ is at a distance $x$ from the center of a uniform thin ring of mass $M$ and radius $R$ on its axis. The gravitational potential energy is minimum at:

The work done to shift a body of mass $m$ from a circular orbit of radius $r$ to $2r$ around Earth is $W$. What is the work done to shift it from $2r$ to $3r$?

In the formula $v_o = \sqrt{GM/r}$, the 'r' represents:

A body is projected vertically upwards. At what point does its total mechanical energy become zero (considering potential energy at infinity is zero)?

When a satellite is moving in a circular orbit, the work done by the gravitational force is:

If the orbital speed of a satellite is $v_o$, what happens if its speed is increased to $\sqrt{2} v_o$?

The escape velocity of a body from the Earth is $v_e$. If the radius of Earth is $R$, then the escape velocity at a height $h=R$ from the surface is:

The orbital velocity of a satellite is $7 \text{ km/s}$. If its speed is increased by $42\%$, it will:

A body is dropped from a height $R$ (radius of Earth) from the surface. With what speed does it hit the ground?

The orbital velocity of a satellite at a height $h$ is $v$. What is the escape velocity from that same height?

A body is projected with escape velocity $v_e$ from the Earth's surface. What is its total energy at the point of projection?

Two satellites revolve around a planet in orbits of radius $R$ and $R + \Delta R$ (where $\Delta R \ll R$). The difference in their orbital velocities $\Delta v$ is approximately:

Which of these is the correct value of $G$ up to three significant figures?

The constant $G$ was introduced in Newton's famous book named:

Is $G$ a vector or a scalar?

Which of the following is the correct name for $G$?

If a graph is plotted between the gravitational force $F$ and $1/r^2$ for two constant masses, the slope of the graph will be:

The constant $G$ is related to the Planck length $l_p$, the Planck mass $m_p$, and the Planck time $t_p$. Which of the following is a correct dimensional check for $G$?

If the force of gravity between two objects of mass $1 \text{ kg}$ each is $F$, what is the distance between them (approximate)?

If the gravitational constant $G$ was $10$ times larger than its current value, which of the following would be true for the Earth?

A uniform thin spherical shell of mass $M$ and radius $R$ has a point mass $m$ inside it at a distance $r < R$ from the center. The gravitational force on $m$ is:

Which of the following is NOT a property of the gravitational constant $G$?

The value of gravitational acceleration $g$ inside a satellite is:

What is the shape of the orbit of a satellite according to Kepler's First Law?

The binding energy of a satellite orbiting Earth is always:

A geostationary satellite must revolve in the same direction as Earth. This direction is:

The energy required to move a satellite of mass $m$ from an orbit of radius $2R$ to $3R$ is:

If the radius of the Earth is $R$, the height of a satellite whose time period is the same as the Earth's rotation is approximately:

Which of the following is NOT a characteristic of a geostationary satellite?

A satellite is orbiting the Earth in a circular path of radius $R$ with an orbital speed $v = \sqrt{GM/R}$. A short-duration firing of its engine changes the direction of its velocity by an angle $\alpha$ relative to the original tangential direction, while the magnitude of the speed remains constant. What is the eccentricity $e$ of the new elliptical orbit?

A satellite is orbiting Earth at a height $h$. If the weight of the satellite on the Earth's surface is $w$, its weight in the orbit is:

The time period of a satellite in a circular orbit around a planet of radius $R$ is $T$. If the satellite is in an orbit very close to the planet, the density of the planet is:

The graph of Potential Energy ($U$) vs distance ($r$) from Earth's center for $r > R$ is a:

The kinetic energy of a satellite is always:

If the distance $r$ between the Earth and satellite is doubled, the potential energy becomes:

In the formula $E = -\frac{GMm}{2r}$, the term $M$ represents:

A satellite of mass $m$ is orbiting at a height $h$ from the Earth's surface. If $R$ is the Earth's radius, its kinetic energy is:

The magnitude of the gravitational potential energy of a satellite is $B$. Its binding energy is:

The orbital speed of a satellite is $v$. What is the speed required for it to escape from the same orbit?

A satellite of mass $m$ orbits a planet of mass $M$ and radius $R$ at a height $h$. If it is moved to a height $2h$, the change in potential energy is:

For a satellite in an elliptical orbit, which of the following remains constant throughout its motion?

If the earth's gravitational constant $G$ were to decrease with time, the radius of a satellite's orbit would: