Question 1

Which of the following statements about gravitational potential energy is correct?

Accepted Answer

Correct Option: B. Solution: Gravitational potential energy is defined as negative and approaches zero as the distance from the Earth approaches infinity.

Question 2

A satellite is in a circular orbit at a height $h$ above the Earth's surface. If the height is doubled, how does the speed of the satellite change?

Accepted Answer

Correct Option: C. Solution: The speed of a satellite in orbit is given by $V = \sqrt{\frac{GM_E}{R_E + h}}$. Doubling the height $h$ increases the denominator, thus decreasing the speed.

Question 3

What is the escape velocity from the surface of a planet with mass $M$ and radius $R$?

Accepted Answer

Correct Option: A. Solution: Escape velocity is derived from setting kinetic energy equal to gravitational potential energy: $v = \sqrt{\frac{2GM}{R}}$.

Question 4

According to Kepler's First Law, what is the shape of the orbit of planets around the Sun?

Accepted Answer

Correct Option: B. Solution: Kepler's First Law states that all planets move in elliptical orbits with the Sun situated at one of the foci.

Question 5

If a planet orbits the Sun with a period half that of Earth's, what is its orbital radius compared to Earth's?

Accepted Answer

Correct Option: B. Solution: According to Kepler's third law, $T^2 \propto a^3$. If the period is half, $\left(\frac{1}{2}\right)^2 = \left(\frac{a}{a_E}\right)^3$. Solving gives $a = 0.71 a_E$.

Question 6

What is the escape speed from the surface of the Earth, given the gravitational constant $G$, the mass of the Earth $M_E$, and the radius of the Earth $R_E$?

Accepted Answer

Correct Option: A. Solution: The escape speed from the surface of the Earth is given by $v_e = \sqrt{\frac{2GM_E}{R_E}}$. This is the minimum speed needed for an object to break free from the gravitational attraction of the Earth without any additional propulsion.

Question 7

If a particle is inside a uniform spherical shell, what is the gravitational force on the particle?

Accepted Answer

Correct Option: A. Solution: The gravitational force on a particle inside a uniform spherical shell is zero due to the symmetry of the shell.

Question 8

Which of the following best describes the method used by Cavendish to measure the gravitational constant $G$?

Accepted Answer

Correct Option: B. Solution: Cavendish used a torsion balance to measure the force between large and small lead spheres, allowing the calculation of the gravitational constant $G$.

Question 9

In Cavendish's experiment to measure the gravitational constant $G$, two large lead spheres are placed near two small lead spheres. What is the primary purpose of the large spheres in this setup?

Accepted Answer

Correct Option: A. Solution: The large spheres are used to exert a gravitational force on the small spheres, creating a torque that twists the wire. This torque is used to calculate the gravitational constant $G$.

Question 10

A satellite is launched from the Earth's surface. If the escape speed is 11.2 km/s, what would be the speed of the satellite far away from the Earth if it is launched with a speed of 33.6 km/s?

Accepted Answer

Correct Option: A. Solution: If a body is projected with thrice the escape speed, the excess speed at infinity can be calculated using energy conservation. The speed far away will be 11.2 km/s, as the excess kinetic energy will convert to speed at infinity.

Question 11

A satellite orbits the Earth at a height of 400 km above the surface. If the mass of the satellite is 200 kg, how much energy is required to move it out of Earth's gravitational influence?

Accepted Answer

Correct Option: C. Solution: The energy required is calculated using the formula for gravitational potential energy and escape velocity. The correct calculation yields approximately 5.8 x $10^9$ J.

Question 12

Consider a system of four particles each of mass $m$ placed at the vertices of a square of side $l$. What is the gravitational potential energy of the system?

Accepted Answer

Correct Option: C. Solution: The potential energy between each pair of masses is $-\frac{Gm^2}{r}$, where $r$ is the distance between them. For four masses at the vertices of a square, there are four pairs at distance $l$ and two diagonal pairs at distance $\sqrt{2}l$. Therefore, the total potential energy is $4\left(-\frac{Gm^2}{l}\right) + 2\left(-\frac{Gm^2}{\sqrt{2}l}\right) = -\frac{6Gm^2}{l}$.

Question 13

Which of the following best describes Kepler's Second Law of Planetary Motion?

Accepted Answer

Correct Option: B. Solution: Kepler's Second Law, or the Law of Areas, states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time, meaning planets move faster when they are closer to the Sun.

Question 14

What is the escape speed required for an object to break free from Earth's gravitational pull without further propulsion?

Accepted Answer

Correct Option: C. Solution: The escape speed from the surface of the Earth is approximately 11.2 km/s, which is the minimum speed required to overcome Earth's gravitational attraction without additional propulsion.

Question 15

If the gravitational force between two objects is $F$, what happens to the force if the distance between them is doubled?

Accepted Answer

Correct Option: D. Solution: According to the inverse square law, if the distance is doubled, the force is reduced to one-fourth.

Question 16

A satellite in a circular orbit has a kinetic energy of $K$ and potential energy of $U$. What is the relationship between $K$ and $U$?

Accepted Answer

Correct Option: A. Solution: For a satellite in a circular orbit, the kinetic energy $K$ is half the magnitude of the potential energy $U$, but with opposite sign, i.e., $K = -\frac{U}{2}$. This results in the total energy being $E = K + U = -\frac{U}{2}$.

Question 17

What is the escape speed from the surface of the Earth if the gravitational constant $G$ is $6.67 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$, the mass of the Earth $M_E$ is $6.0 	imes 10^{24} 	ext{ kg}$, and the radius of the Earth $R_E$ is $6.4 	imes 10^6 	ext{ m}$?

Accepted Answer

Correct Option: B. Solution: The escape speed $v_e$ is given by $v_e = \sqrt{\frac{2G M_E}{R_E}}$. Substituting the given values, $v_e = \sqrt{\frac{2 	imes 6.67 	imes 10^{-11} 	imes 6.0 	imes 10^{24}}{6.4 	imes 10^6}} = 11.2 	ext{ km/s}$.

Question 18

According to Newton's Universal Law of Gravitation, if the distance between two masses is doubled, how does the gravitational force between them change?

Accepted Answer

Correct Option: D. Solution: The gravitational force is inversely proportional to the square of the distance between the masses. Doubling the distance reduces the force to one-fourth.

Question 19

If a particle is placed at a depth $d$ below the Earth's surface, how does the gravitational acceleration $g(d)$ compare to the gravitational acceleration $g$ at the surface?

Accepted Answer

Correct Option: A. Solution: The gravitational acceleration at a depth $d$ is given by $g(d) = g \left(1 - \frac{d}{R_E}\right)$, indicating that gravity decreases linearly with depth.

Question 20

Which of the following statements about Kepler's Laws is incorrect?

Accepted Answer

Correct Option: B. Solution: Kepler's Second Law implies that a planet's speed varies, being faster when closer to the Sun and slower when farther away, not constant.

Question 21

Consider a hypothetical planet that has a mass $M$ and radius $R$. If the gravitational force on a 1 kg object on the surface of this planet is $G \frac{M}{R^2}$, what would be the gravitational force on the same object at a height $R$ above the surface of the planet?

Accepted Answer

Correct Option: A. Solution: The gravitational force at a distance $r$ from the center of a planet is given by $F = G \frac{M}{r^2}$. At a height $R$ above the surface, the distance from the center is $2R$. Thus, the force is $F = G \frac{M}{(2R)^2} = G \frac{M}{4R^2}$.

Question 22

A satellite is in a circular orbit of radius $2R_E$ about the Earth. How much energy is required to transfer it to a circular orbit of radius $4R_E$?

Accepted Answer

Correct Option: A. Solution: The change in energy is calculated using the formula for gravitational potential energy, and the difference between the two orbits is $\Delta E = \frac{G M_E m}{8R_E}$.

Question 23

A satellite is orbiting Earth at a height where the acceleration due to gravity is half of that on the surface. What is the approximate height of the satellite above the Earth's surface?

Accepted Answer

Correct Option: D. Solution: The acceleration due to gravity decreases with height. At a height of approximately $1.5R_E$, the acceleration is half of that on the surface.

Question 24

If a satellite's orbit becomes elliptical, how does its total energy change?

Accepted Answer

Correct Option: C. Solution: In an elliptical orbit, the total energy remains negative, similar to a circular orbit, as satellites are bound systems.

Question 25

A satellite is orbiting the Earth at a height $h$ above the surface. If the radius of the Earth is $R_E$ and the gravitational constant is $G$, what is the expression for the total mechanical energy of the satellite?

Accepted Answer

Correct Option: A. Solution: The total mechanical energy of a satellite in a circular orbit is given by $E = -\frac{GM_E m}{2(R_E + h)}$, where $M_E$ is the mass of the Earth, $m$ is the mass of the satellite, and $h$ is the height above the Earth's surface.

Question 26

What is the time period of a satellite orbiting very close to the Earth's surface?

Accepted Answer

Correct Option: B. Solution: For a satellite very close to the Earth's surface, the time period is approximately 85 minutes.

Question 27

What is the gravitational potential energy associated with two particles of masses $m_1$ and $m_2$ separated by a distance $r$?

Accepted Answer

Correct Option: A. Solution: The gravitational potential energy $V$ is given by $V = -\frac{G m_1 m_2}{r}$, where $G$ is the gravitational constant.

Question 28

A satellite is orbiting the Earth at a height of $400 	ext{ km}$ above the surface. How does the gravitational force on the satellite compare to that on the surface?

Accepted Answer

Correct Option: B. Solution: The gravitational force decreases with height above the Earth's surface, so it is less than on the surface.

Question 29

A planet is observed to sweep equal areas in equal intervals of time as it orbits the Sun. Which of Kepler's laws does this observation confirm?

Accepted Answer

Correct Option: B. Solution: Kepler's Second Law, also known as the Law of Areas, states that the line joining a planet to the Sun sweeps out equal areas in equal intervals of time.

Question 30

What is the resultant gravitational force on a point mass $m_1$ due to two other point masses $m_2$ and $m_3$ placed at equal distances from $m_1$ in opposite directions?

Accepted Answer

Correct Option: A. Solution: The forces exerted by $m_2$ and $m_3$ on $m_1$ cancel each other out due to symmetry, resulting in a net force of zero.

Question 31

A satellite is orbiting the Earth at a height $h$ above the surface. Which of the following expressions correctly describes the gravitational potential energy $U$ of the satellite?

Accepted Answer

Correct Option: A. Solution: The gravitational potential energy of a satellite at a height $h$ is given by $U = -\frac{G M_E m}{R_E + h}$, where $M_E$ is the Earth's mass and $R_E$ is the Earth's radius.

Question 32

Why do astronauts experience weightlessness in a space satellite?

Accepted Answer

Correct Option: B. Solution: Astronauts experience weightlessness because both the astronaut and the satellite are in free fall towards the Earth, not because gravity is absent.

Question 33

In Cavendish's experiment to determine the gravitational constant $G$, what role does the angle of twist $\Theta$ play?

Accepted Answer

Correct Option: B. Solution: The angle of twist $\Theta$ is used to calculate the restoring torque of the wire, which balances the gravitational torque, allowing the determination of $G$.

Question 34

Kepler's Third Law relates the square of the orbital period of a planet to which of the following?

Accepted Answer

Correct Option: B. Solution: Kepler's Third Law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Question 35

A satellite is orbiting Earth at a height where the acceleration due to gravity is half of that on the surface. If the radius of Earth is $R_E$, at what height $h$ is the satellite orbiting?

Accepted Answer

Correct Option: A. Solution: The gravitational force decreases with the square of the distance. If gravity is half, the satellite is at a distance of $\sqrt{2} R_E$ from the center, which means $h = R_E$.

Question 36

If a satellite is to escape Earth's gravitational field, which of the following must be true about its kinetic energy at launch?

Accepted Answer

Correct Option: B. Solution: For a satellite to escape Earth's gravitational field, its kinetic energy must be greater than the gravitational potential energy at launch, ensuring that the total mechanical energy is non-negative.

Question 37

According to Kepler's First Law, what is the shape of the orbit of planets around the Sun?

Accepted Answer

Correct Option: B. Solution: Kepler's First Law states that all planets move in elliptical orbits with the Sun situated at one of the foci.

Question 38

If the gravitational potential energy at infinity is taken as zero, what is the gravitational potential energy of a mass $m$ at a distance $r$ from the center of Earth?

Accepted Answer

Correct Option: A. Solution: Gravitational potential energy is given by $V = -\frac{G M_E m}{r}$, where $G$ is the gravitational constant, $M_E$ is Earth's mass, and $r$ is the distance from the center.

Question 39

According to Kepler's third law, how is the square of the orbital period of a planet related to the semi-major axis of its orbit?

Accepted Answer

Correct Option: C. Solution: Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Question 40

An object is projected from the surface of the Earth with a speed equal to the escape speed. Which of the following statements is true about the object's motion?

Accepted Answer

Correct Option: B. Solution: The escape speed is the minimum speed required for an object to break free from the gravitational attraction of a celestial body without further propulsion. Therefore, if an object is projected with this speed, it will reach infinity with zero speed.

Question 41

A satellite is orbiting the Earth at a height of $400 	ext{ km}$ above the surface. If the mass of the Earth is $6.0 	imes 10^{24} 	ext{ kg}$ and the radius of the Earth is $6.4 	imes 10^6 	ext{ m}$, what is the gravitational potential energy of the satellite of mass $200 	ext{ kg}$ at this height?

Accepted Answer

Correct Option: B. Solution: The gravitational potential energy is given by $U = -\frac{G M_E m}{R_E + h}$. Substituting the given values, $U = -\frac{6.67 	imes 10^{-11} 	imes 6.0 	imes 10^{24} 	imes 200}{6.4 	imes 10^6 + 400 	imes 10^3} = -7.84 	imes 10^9 	ext{ J}$.

Question 42

A satellite is in a circular orbit of radius $2R_E$ about the Earth. How much energy is required to transfer it to a circular orbit of radius $4R_E$?

Accepted Answer

Correct Option: A. Solution: The energy of a satellite in orbit is given by $E = -\frac{GmM_E}{2r}$. The change in energy when moving from $r = 2R_E$ to $r = 4R_E$ is $E_2 - E_1 = -\frac{GmM_E}{2 	imes 4R_E} + \frac{GmM_E}{2 	imes 2R_E} = \frac{3GmM_E}{8R_E}$.

Question 43

If the escape speed from the Earth's surface is $11.2 	ext{ km/s}$, what would be the escape speed from a planet with twice the Earth's radius and the same density?

Accepted Answer

Correct Option: B. Solution: The escape speed $v_e$ is given by $v_e = \sqrt{\frac{2GM}{R}}$. If the radius is doubled and density remains the same, the mass becomes 8 times larger, hence $v_e$ becomes $\sqrt{8} 	imes 11.2 = 22.4 	ext{ km/s}$.

Question 44

Consider a rocket fired vertically from the Earth's surface with a speed of $5 	ext{ km/s}$. How far from the Earth does the rocket go before returning, if the mass of the Earth is $6.0 	imes 10^{24} 	ext{ kg}$ and the mean radius of the Earth is $6.4 	imes 10^6 	ext{ m}$?

Accepted Answer

Correct Option: A. Solution: Using the energy conservation principle, the maximum height $h$ is found using $\frac{1}{2}mv^2 = \frac{G M_E m}{R_E + h}$. Solving for $h$ gives $h = 1.28 	imes 10^7 	ext{ m}$.

Question 45

For a planet orbiting the Sun, which of the following statements about its gravitational potential energy is true?

Accepted Answer

Correct Option: B. Solution: The gravitational potential energy is negative, as it is defined to be zero at infinity and decreases as the planet approaches the Sun.

Question 46

If a body is projected vertically from the Earth's surface with a speed equal to the escape velocity, what will be its speed at infinity?

Accepted Answer

Correct Option: A. Solution: The escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a massive body without further propulsion. At infinity, the speed becomes zero.

Question 47

A satellite is orbiting Earth at a height $h$ above the surface. Which of the following correctly describes the relationship between the gravitational force acting on the satellite and its orbital speed $V$?

Accepted Answer

Correct Option: A. Solution: The gravitational force provides the centripetal force required for the satellite's circular motion, which is proportional to the square of the orbital speed: $F = \frac{mV^2}{R}$.

Question 48

If a stone is thrown with a speed $V_i$ such that it reaches infinity with zero speed, what is the minimum speed $V_i$ required for escape from the Earth's surface?

Accepted Answer

Correct Option: A. Solution: The minimum speed required for escape is given by $V_i = \sqrt{\frac{2G M_E}{R_E}}$, which is derived from setting the total mechanical energy to zero at infinity.

Question 49

A body weighs $250 	ext{ N}$ on the surface of the Earth. Assuming the Earth to be a sphere of uniform mass density, what would be the weight of the body halfway down to the center of the Earth?

Accepted Answer

Correct Option: A. Solution: The weight of the body at a depth $d$ is given by $W_d = W_0 \left(1 - \frac{d}{R_E}ight)$. At halfway, $d = \frac{R_E}{2}$, so $W_d = 250 	imes \left(1 - \frac{1}{2}ight) = 125 	ext{ N}$.

Question 50

What is the gravitational potential energy of a particle due to gravitational forces?

Accepted Answer

Correct Option: A. Solution: Gravitational potential energy is defined as the work done in bringing a particle from infinity to a point in space.

Question 51

Which of the following statements about gravitational force is true?

Accepted Answer

Correct Option: B. Solution: Gravitational force is always attractive, acting between any two masses.

Question 52

A comet orbits the Sun in a highly elliptical orbit. Which of the following quantities remains constant throughout its orbit?

Accepted Answer

Correct Option: B. Solution: In a gravitational field, angular momentum is conserved for any central force. Therefore, the angular momentum of the comet remains constant throughout its orbit.

Question 53

According to Newton's Universal Law of Gravitation, the force between two masses is proportional to which of the following?

Accepted Answer

Correct Option: B. Solution: Newton's Universal Law of Gravitation states that the force is proportional to the product of the masses and inversely proportional to the square of the distance between them.

Question 54

If a planet's semi-major axis is doubled, how does its orbital period change according to Kepler's Third Law?

Accepted Answer

Correct Option: B. Solution: According to Kepler's Third Law, if the semi-major axis is doubled, the orbital period increases by a factor of $\sqrt{2^3} = \sqrt{8}$, which means the period becomes eight times longer.

Question 55

Consider a planet that orbits the Sun with a period that is half that of Earth's. What is the semi-major axis of its orbit compared to Earth's orbit?

Accepted Answer

Correct Option: B. Solution: According to Kepler's Third Law, $T^2 \propto a^3$. If the period $T$ is half, then $a^3 = (\frac{1}{2})^2 a_{Earth}^3$, so $a = \sqrt[3]{\frac{1}{4}} a_{Earth} = \sqrt[3]{2}^{-1} a_{Earth}$.

Question 56

If the semi-major axis of a planet's orbit is doubled, how does this affect the orbital period according to Kepler's Third Law?

Accepted Answer

Correct Option: D. Solution: Kepler's Third Law states that the square of the orbital period is proportional to the cube of the semi-major axis. Therefore, if the semi-major axis is doubled, the period increases by a factor of $\sqrt{8}$.

Question 57

A planet orbits a star in an elliptical orbit. At which point in its orbit does it have the highest kinetic energy?

Accepted Answer

Correct Option: B. Solution: According to Kepler's second law, a planet moves faster when it is closer to the star, at the perihelion, hence it has the highest kinetic energy at this point.

Question 58

What happens to the acceleration due to gravity as one moves to a depth $d$ below the Earth's surface?

Accepted Answer

Correct Option: B. Solution: The acceleration due to gravity decreases with depth, as given by $g(d) = g(0)(1 - \frac{d}{R_E})$.

Question 59

Consider a hollow spherical shell with a uniform density. If a point mass is placed inside the shell, what is the gravitational force experienced by the point mass?

Accepted Answer

Correct Option: A. Solution: The gravitational force inside a hollow spherical shell is zero due to the symmetry of the shell, causing the forces from all parts of the shell to cancel out.

Question 60

What is the gravitational force exerted by a hollow spherical shell of uniform density on a point mass located inside it?

Accepted Answer

Correct Option: A. Solution: The gravitational force due to a hollow spherical shell of uniform density on a point mass situated inside it is zero. This is because the forces from various regions of the shell cancel each other out completely.

Question 61

A satellite is orbiting Earth at a height where the gravitational force is half of its value at the surface. What is the approximate height of the satellite above Earth's surface?

Accepted Answer

Correct Option: A. Solution: The gravitational force decreases with the square of the distance from the center of the Earth. If the force is half, the distance must be $\sqrt{2}R_E$, which means the height above the surface is $\sqrt{2}R_E - R_E \approx R_E$.

Question 62

What is the total mechanical energy of a satellite in a circular orbit around the Earth?

Accepted Answer

Correct Option: C. Solution: The total mechanical energy of a satellite in a circular orbit is negative, as the potential energy is negative and twice the magnitude of the positive kinetic energy.

Question 63

Consider a satellite orbiting Earth at a height $h$ above the surface. If the gravitational potential energy at infinity is zero, what is the total mechanical energy of the satellite?

Accepted Answer

Correct Option: A. Solution: The total mechanical energy of a satellite in orbit is $E = K.E. + P.E. = \frac{1}{2}mv^2 - \frac{GMm}{R_E + h}$. For a circular orbit, $v^2 = \frac{GM}{R_E + h}$, so $E = -\frac{GMm}{2(R_E + h)}$.

Question 64

A satellite is in a circular orbit around the Earth at a distance $R_E + h$ from the center of the Earth. If the gravitational force provides the necessary centripetal force, which equation correctly describes the relationship between the satellite's speed $V$, the Earth's mass $M_E$, and the gravitational constant $G$?

Accepted Answer

Correct Option: A. Solution: The centripetal force required for the satellite's orbit is provided by the gravitational force, leading to the equation $V^2 = \frac{GM_E}{R_E + h}$.

Gravitation

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Kepler's Laws of Planetary Motion

Universal Law of Gravitation

Gravitational Potential Energy

Escape Speed

Acceleration Due to Gravity

Energy of an Orbiting Satellite

Gravitational Constant Measurement

Gravitational Force in Spherical Shells

Superposition of Gravitational Forces

Gravitational Potential

Earth Satellites and Orbital Motion

Weightlessness and Free Fall in Satellites

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Kepler's Laws of Planetary Motion

Universal Law of Gravitation

Gravitational Potential Energy

Escape Speed

Acceleration Due to Gravity

Energy of an Orbiting Satellite

Gravitational Constant Measurement

Gravitational Force in Spherical Shells

Superposition of Gravitational Forces

Gravitational Potential

Earth Satellites and Orbital Motion

Weightlessness and Free Fall in Satellites

AI Learning Assistant

Practice Test – MCQs, True/False

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Multiple Choice Questions

Q1.Which of the following statements about gravitational potential energy is correct?

Correct Answer: B

Q2.A satellite is in a circular orbit at a height hhh above the Earth's surface. If the height is doubled, how does the speed of the satellite change?

Correct Answer: C

Q3.What is the escape velocity from the surface of a planet with mass MMM and radius RRR?

Correct Answer: A

Q4.According to Kepler's First Law, what is the shape of the orbit of planets around the Sun?

Correct Answer: B

Q5.If a planet orbits the Sun with a period half that of Earth's, what is its orbital radius compared to Earth's?

Correct Answer: B

Q6.What is the escape speed from the surface of the Earth, given the gravitational constant GGG, the mass of the Earth MEM_EME​, and the radius of the Earth RER_ERE​?

Correct Answer: A

Q7.If a particle is inside a uniform spherical shell, what is the gravitational force on the particle?

Correct Answer: A

Q8.Which of the following best describes the method used by Cavendish to measure the gravitational constant GGG?

Correct Answer: B

Q9.In Cavendish's experiment to measure the gravitational constant GGG, two large lead spheres are placed near two small lead spheres. What is the primary purpose of the large spheres in this setup?

Correct Answer: A

Q10.A satellite is launched from the Earth's surface. If the escape speed is 11.2 km/s, what would be the speed of the satellite far away from the Earth if it is launched with a speed of 33.6 km/s?

Correct Answer: A

Q11.A satellite orbits the Earth at a height of 400 km above the surface. If the mass of the satellite is 200 kg, how much energy is required to move it out of Earth's gravitational influence?

Correct Answer: C

Q12.Consider a system of four particles each of mass mmm placed at the vertices of a square of side lll. What is the gravitational potential energy of the system?

Correct Answer: C

Q13.Which of the following best describes Kepler's Second Law of Planetary Motion?

Correct Answer: B

Q14.What is the escape speed required for an object to break free from Earth's gravitational pull without further propulsion?

Correct Answer: C

Q15.If the gravitational force between two objects is FFF, what happens to the force if the distance between them is doubled?

Correct Answer: D

Q16.A satellite in a circular orbit has a kinetic energy of KKK and potential energy of UUU. What is the relationship between KKK and UUU?

Correct Answer: A

Correct Answer: B

Q18.According to Newton's Universal Law of Gravitation, if the distance between two masses is doubled, how does the gravitational force between them change?

Correct Answer: D

Q19.If a particle is placed at a depth ddd below the Earth's surface, how does the gravitational acceleration g(d)g(d)g(d) compare to the gravitational acceleration ggg at the surface?

Correct Answer: A

Q20.Which of the following statements about Kepler's Laws is incorrect?

Correct Answer: B

Q21.Consider a hypothetical planet that has a mass MMM and radius RRR. If the gravitational force on a 1 kg object on the surface of this planet is GMR2G \frac{M}{R^2}GR2M​, what would be the gravitational force on the same object at a height RRR above the surface of the planet?

Correct Answer: A

Q22.A satellite is in a circular orbit of radius 2RE2R_E2RE​ about the Earth. How much energy is required to transfer it to a circular orbit of radius 4RE4R_E4RE​?

Correct Answer: A

Q23.A satellite is orbiting Earth at a height where the acceleration due to gravity is half of that on the surface. What is the approximate height of the satellite above the Earth's surface?

Correct Answer: D