Question 1

When a falling meteor is at a distance above the Earth's surface of 3 times the Earth's radius, what is its acceleration due to the Earth's gravity?

Accepted Answer

0.613 m/s2

Question 2

What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun?

Accepted Answer

0.50 year

Question 3

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 * 106 m, mass = 6.0 * 1024 kg) with a period of 5.0 h?

Accepted Answer

A) 88 N 
B) 55 N 
C) 36 N 
D) 98 N 
E) 18 N 
A) 88 N 
B) 55 N 
C) 36 N 
D) 98 N 
E) 18 N C

Question 4

A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

Accepted Answer

A) GmM/(2R) 
B) GmM/(3R) 
C) GmM/(4R) 
D) GmM/(6R) 
E) 3GmM/(4R) 
A) GmM/(2R) 
B) GmM/(3R) 
C) GmM/(4R) 
D) GmM/(6R) 
E) 3GmM/(4R)

Question 5

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to:

Accepted Answer

A) r. 
B) r2. 
C) r3. 
D) r4. 
E) r6. 
A) r. 
B) r2. 
C) r3. 
D) r4. 
E) r6.

Question 6

Suppose the gravitational force of the Earth on a body was   . What escape velocity ve would a body need to escape the gravitational field of the Earth?

Accepted Answer

A)  $v_{e}=\sqrt{\frac{K M_{E}}{2 R_{E}^{2}}}$ . 
B)  $v_{e}=\sqrt{\frac{K M_{E}}{R_{E}^{2}}}$ . 
C)  $v_{e}=\sqrt{\frac{K M_{E}}{2 R_{E}}}$ . 
D)  $v_{e}=\sqrt{\frac{K M_{E}}{R_{E}}}$ . 
E)  $v_{e}=\sqrt{K  M_{E}}$ . 
A)  $v_{e}=\sqrt{\frac{K M_{E}}{2 R_{E}^{2}}}$ . 
B)  $v_{e}=\sqrt{\frac{K M_{E}}{R_{E}^{2}}}$ . 
C)  $v_{e}=\sqrt{\frac{K M_{E}}{2 R_{E}}}$ . 
D)  $v_{e}=\sqrt{\frac{K M_{E}}{R_{E}}}$ . 
E)  $v_{e}=\sqrt{K  M_{E}}$ .

Question 7

The figure below shows a planet travelling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A:

Accepted Answer

A) its speed is constant. 
B) its speed is increasing. 
C) its speed is decreasing. 
D) its speed is a maximum. 
E) its speed is a minimum. 
A) its speed is constant. 
B) its speed is increasing. 
C) its speed is decreasing. 
D) its speed is a maximum. 
E) its speed is a minimum.

Question 8

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2* 107 m. If the radius of Roton is 5.0* 106 m, what is the magnitude of the free-fall acceleration on the surface of Roton?

Accepted Answer

A) 31 m/s2 
B) 27 m/s2 
C) 34 m/s2 
D) 40 m/s2 
E) 19 m/s2 
A) 31 m/s2 
B) 27 m/s2 
C) 34 m/s2 
D) 40 m/s2 
E) 19 m/s2

Question 9

A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet?

Accepted Answer

A)  $\frac{G m M}{24 R}$ 
B)  $\frac{G m M}{15 R}$ 
C)  $\frac{G m M}{12 R}$ 
D)  $\frac{2 G m M}{21 R}$ 
E)  $\frac{3 G m M}{5 R}$ 
A)  $\frac{G m M}{24 R}$ 
B)  $\frac{G m M}{15 R}$ 
C)  $\frac{G m M}{12 R}$ 
D)  $\frac{2 G m M}{21 R}$ 
E)  $\frac{3 G m M}{5 R}$

Question 10

Refer to Exhibit 11-1 below.Exhibit 11-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure.   What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m, y = 0?

Accepted Answer

A) 2.2 * 10-8 N 
B) 1.9 *10-8 N 
C) 1.4 * 10-8 N 
D) 1.6 * 10-8 N 
E) 2.5 * 10-8 N 
A) 2.2 * 10-8 N 
B) 1.9 *10-8 N 
C) 1.4 * 10-8 N 
D) 1.6 * 10-8 N 
E) 2.5 * 10-8 N

Question 11

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have:

Accepted Answer

A) the smaller period. 
B) the greater period. 
C) the smaller gravitational mass. 
D) the larger gravitational mass. 
E) the larger universal gravitational constant. 
A) the smaller period. 
B) the greater period. 
C) the smaller gravitational mass. 
D) the larger gravitational mass. 
E) the larger universal gravitational constant.

Question 12

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

Accepted Answer

A) 4 years 
B) 8 years 
C) 16 years 
D) 32 years 
E) 64 years 
A) 4 years 
B) 8 years 
C) 16 years 
D) 32 years 
E) 64 years

Question 13

Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

Accepted Answer

A) 0.41 D 
B) 0.33 D 
C) 0.37 D 
D) 0.29 D 
E) 0.14 D 
A) 0.41 D 
B) 0.33 D 
C) 0.37 D 
D) 0.29 D 
E) 0.14 D

Question 14

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (RE = 6.37 * 106 m; RM = 1.74 *106 m; ME = 5.98 *1024 kg; MM = 7.36 *1022 kg.)

Accepted Answer

A) 6.03* 10-3 min. 
B) 0.713 min. 
C) 84.3 min. 
D) 108 min. 
E) 140 min. 
A) 6.03* 10-3 min. 
B) 0.713 min. 
C) 84.3 min. 
D) 108 min. 
E) 140 min.

Question 15

At the moment of a total eclipse, the moon lies along a line from the Earth to the sun. If your normal weight is 600 N, how much is your weight decreased by the combined pull of the sun and moon?
MSUN = 2.0 * 1030 kg,
rS-E = 1.5 *108 km
MMOON = 7.4 * 1022 kg,
rM-E = 3.8 * 105 km

Accepted Answer

The answer of At the moment of a total eclipse,...

Question 16

A satellite revolves around the Earth in a circular orbit with a mechanical energy of $-10^{12}$ J. What is its kinetic energy?

Accepted Answer

A)  $-5 \times 10^{11} \mathrm{~J}$ 
B)  $+5 \times 10^{11} \mathrm{~J}$ 
C)  $+10 \times 10^{11} \mathrm{~J}$ 
D)  $-20 \times 10^{11} \mathrm{~J}$ 
E)  $+7.1 \times 10^{11} \mathrm{~J}$ 
A)  $-5 \times 10^{11} \mathrm{~J}$ 
B)  $+5 \times 10^{11} \mathrm{~J}$ 
C)  $+10 \times 10^{11} \mathrm{~J}$ 
D)  $-20 \times 10^{11} \mathrm{~J}$ 
E)  $+7.1 \times 10^{11} \mathrm{~J}$

Question 17

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?

Accepted Answer

A) There is no gravitational force on the satellite. 
B) There is no acceleration toward the centre of the Earth. 
C) The satellite is in a state of free fall toward the Earth. 
D) There is a tangential force that helps the satellite keep up with the rotation of the Earth. 
E) The force toward the centre of the Earth is balanced by a force away from the centre of the Earth. 
A) There is no gravitational force on the satellite. 
B) There is no acceleration toward the centre of the Earth. 
C) The satellite is in a state of free fall toward the Earth. 
D) There is a tangential force that helps the satellite keep up with the rotation of the Earth. 
E) The force toward the centre of the Earth is balanced by a force away from the centre of the Earth.

Question 18

The figure below shows a planet travelling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A:

Accepted Answer

A) its speed is decreasing. 
B) its angular momentum is increasing. 
C) the gravitational force does no work on the planet. 
D) all of the above are correct. 
E) none of the above is correct. 
A) its speed is decreasing. 
B) its angular momentum is increasing. 
C) the gravitational force does no work on the planet. 
D) all of the above are correct. 
E) none of the above is correct.

Question 19

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 * 106 m, mass = 6.0 * 1024 kg)

Accepted Answer

A) 2.9 *108 J 
B) 3.5 * 108 J 
C) 4.1 * 108 J 
D) 4.7* 108 J 
E) 5.9 * 108 J 
A) 2.9 *108 J 
B) 3.5 * 108 J 
C) 4.1 * 108 J 
D) 4.7* 108 J 
E) 5.9 * 108 J

Question 20

Isaac Newton was able to estimate a value for G, the universal gravitational constant, from the following data: the radius of the Earth is about 6400 km, the average density of rocks is about 5.50 g/cm3, and g = 9.80 m/s2 near the surface of the Earth. What value did Newton obtain for G?

Accepted Answer

6.65 *10-1

Exam 11: Gravity

When a falling meteor is at a distance above the Earth's surface of 3 times the Earth's radius, what is its acceleration due to the Earth's gravity?

What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun?

What is the gravitational force on a 20-kg satellite circling the Earth (radius = 6.4 * 106 m, mass = 6.0 * 1024 kg) with a period of 5.0 h?

A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to:

Suppose the gravitational force of the Earth on a body was . What escape velocity ve would a body need to escape the gravitational field of the Earth?

The figure below shows a planet travelling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A:

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2* 107 m. If the radius of Roton is 5.0* 106 m, what is the magnitude of the free-fall acceleration on the surface of Roton?

A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet?

Refer to Exhibit 11-1 below.Exhibit 11-1 Three 5.0-kg masses are located at points in the xy plane as shown in the figure. What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m, y = 0?

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have:

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (RE = 6.37 * 106 m; RM = 1.74 *106 m; ME = 5.98 *1024 kg; MM = 7.36 *1022 kg.)

At the moment of a total eclipse, the moon lies along a line from the Earth to the sun. If your normal weight is 600 N, how much is your weight decreased by the combined pull of the sun and moon? MSUN = 2.0 * 1030 kg, rS-E = 1.5 *108 km MMOON = 7.4 * 1022 kg, rM-E = 3.8 * 105 km

A satellite revolves around the Earth in a circular orbit with a mechanical energy of −1012-10^{12}−1012 J. What is its kinetic energy?

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?

The figure below shows a planet travelling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A:

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 * 106 m, mass = 6.0 * 1024 kg)

Isaac Newton was able to estimate a value for G, the universal gravitational constant, from the following data: the radius of the Earth is about 6400 km, the average density of rocks is about 5.50 g/cm3, and g = 9.80 m/s2 near the surface of the Earth. What value did Newton obtain for G?

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The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (RE = 6.37 * 106 m; RM = 1.74 106 m; ME = 5.98 1024 kg; MM = 7.36 *1022 kg.)

At the moment of a total eclipse, the moon lies along a line from the Earth to the sun. If your normal weight is 600 N, how much is your weight decreased by the combined pull of the sun and moon? MSUN = 2.0 * 1030 kg, rS-E = 1.5 108 km MMOON = 7.4 1022 kg, rM-E = 3.8 * 105 km

A satellite revolves around the Earth in a circular orbit with a mechanical energy of $-10^{12}$ J. What is its kinetic energy?