Question 1

An asteroid has been discovered revolving around the Sun on a circular orbit with radius 4.2 times the radius of the Earth's orbit around the Sun (which is about 149.6 million kilometers).Knowing that it takes the Earth 1 year to complete a revolution,how many years does it take for that asteroid?

Accepted Answer

A) 0.041 
B) 0.32 
C) 1 
D) 5.3 
E) 8.6

Question 2

When the Moon is directly between the Earth and the Sun,what is the ratio of the force on the Moon due to the Earth to the force on the Moon due to the Sun? The masses of Sun,Earth,and Moon are 1.99 * 1030 kg,5.97 * 1024 kg,and 7.36 * 1022 kg,respectively.The Earth-Moon distance is 3.84 *108 m,while the Earth-Sun distance is 1.51 * 1011 m.

Accepted Answer

A) 2.2 
B) 0.46 
C) 847 
D) 1.2 * 10-3

Question 3

What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 1024 kg,radius R = 106 m,and the center-to-center distance between any two planets is 10 R.

Accepted Answer

A) 1.04 km/s 
B) 8.33 km/s 
C) 2.35 km/s 
D) 12.6 km/s 
E) 3.96 km/s

Question 4

An imaginary planet has a mass of 8.00 * 1023 kg and a diameter of 5.0 * 106 m.What is the escape speed from the surface of this planet?

Accepted Answer

A) 3.5 km/s 
B) 4.8 km/s 
C) 5.7 km/s 
D) 6.5 km/s 
E) 7.2 km/s

Question 5

The figure shows a system of three masses.What is the magnitude of the gravitational force on the 10-kg mass? The center-to-center distances between masses are shown in the diagram.

Accepted Answer

A) 4.96 * 10-8 N 
B) 4.10 * 10-8 N 
C) 5.34 * 10-8 N 
D) 6.56 * 10-8 N 
E) 9.05 * 10-8 N

Question 6

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 * 108 m/s).What is the radius of a 24 solar mass black hole?

Accepted Answer

A) 6.3 * 106 m 
B) 7.1 * 104 m 
C) 5.4 * 105 m 
D) 7.0 * 108 m 
E) 2.2 * 107 m

Question 7

A 51-kg satellite is put into orbit and has 152 MJ of kinetic energy.How high above the Earth's surface is the orbit?

Accepted Answer

A) 60,400 km 
B) 37,000 km 
C) 74,000 km 
D) 53,100 km 
E) 86,200 km

Question 8

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

Accepted Answer

A) It is possible to have a satellite traveling either at high speed or at low speed in a given circular orbit. 
B) Only circular orbits,not elliptical ones,are possible for artificial satellites. 
C) A satellite of a large diameter circular orbit will always have a longer period of revolution than will a satellite with smaller diameter orbit. 
D) The velocity required to keep a satellite in a given orbit depends on the mass of the satellite. 
E) The period of revolution of a satellite is independent of the radius of its orbit.

Question 9

Given the mean distance between the Moon and the Earth is 3.84 * 108 m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 1022 kg on a 70-kg man standing on the surface of the Earth.

Accepted Answer

A) 2.33 * 10-3 N 
B) 5.89 * 10-2 N 
C) 9.81 * 10-2 N 
D) 0.75 N 
E) 5.2 N

Question 10

Two identical 10.0-kg point masses are held a distance of 20.0 cm apart.If one of the masses is released and allowed to fall toward the other mass,what is the acceleration of the mass just as it is released? Assume that the only force acting on the masses is the gravitational force of the other mass.

Accepted Answer

A) 0.330 * 10-8 m/s2. 
B) 1.67 * 10-8 m/s2. 
C) 3.41 * 10-8 m/s2. 
D) 4.83 * 10-8 m/s2.

Question 11

The radius of the orbit of a planet around a star is proportional to

Accepted Answer

A) the orbital period of the planet. 
B) the square root of the orbital period of the planet. 
C) the square of the orbital period of the planet. 
D) the 3/2 power of the orbital period of the planet. 
E) the 2/3 power of the orbital period of the planet.

Question 12

Two identical point masses are held a distance of 5.0 cm apart.One of the masses is released and allowed to fall toward the other mass.If its initial acceleration just as it is released is 1.67 * 10-8 m/s2,what is the mass of one of these two identical point masses? Assume that the only force acting on the masses is the gravitational force of the other mass.

Accepted Answer

A) 10 kg 
B) 0.63 kg 
C) 1.2 kg 
D) 0.59 kg

Question 13

Two satellites A and B orbit the Earth with the orbital radius of A,RA equal to twice that of B,RA = 2RB.What is the ratio of their masses MA/MB?

Accepted Answer

A) 2 
B) ½ 
C) 4 
D) ¼ 
E) It is impossible to tell.

Question 14

A plumb bob located at latitude 63.0S1U1P1$\circ$S1S1P0 north hangs motionlessly with respect to the ground beneath it.Determine the angle that the string supporting the bob makes with respect to a straight line going through the bob and the center of the Earth.

Accepted Answer

A) 0S1U1P1$\circ$S1S1P0 
B) 0.10S1U1P1$\circ$S1S1P0 
C) 0.20S1U1P1$\circ$S1S1P0 
D) 0.30S1U1P1$\circ$S1S1P0 
E) Sufficient information is not given.

Question 15

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the equator.

Accepted Answer

A) 6.236 * 109 J 
B) 1.077 * 107 J 
C) 6.244 * 109 J 
D) 3.132 * 109 J 
E) 3.121 * 109 J

Question 16

The distance between Earth and the Sun is 149.6 million km,and the distance between Venus and the Sun is 108.2 million km.How long does it take Venus to orbit once around the Sun?

Accepted Answer

A) 0.615 years 
B) 0.723 years 
C) 1 year 
D) 1.38 years 
E) 1.63 years

Question 17

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the north pole.

Accepted Answer

A) 6.236 * 109 J 
B) 1.077 * 109 J 
C) 3.132 * 109 J 
D) 3.121 * 109 J 
E) 6.244 * 109 J

Question 18

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 1024 kg and its radius is 6.37 * 106 m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

Accepted Answer

A) 3.14 * 107 J. 
B) 6.25 * 107 J. 
C) 9.8 * 107 J. 
D) 11.5 * 108 J. 
E) 6.28 * 109 J.

Question 19

An artificial satellite of 104 kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

Accepted Answer

A) 7850 kg/m3. 
B) 5734 kg/m3. 
C) 4205 kg/m3. 
D) 3330 kg/m3. 
E) 2154 kg/m3.

Question 20

If the Earth became 5% bigger in radius (R = 1.05RE)and 10% bigger in mass (M = 1.1ME),about what would the new value of the acceleration of gravity be near the surface of the Earth?

Accepted Answer

A) g 
B) 1.3 g 
C) 0.7 g 
D) 2.0 g 
E) 0.1 g

Exam 12: Gravitation

An asteroid has been discovered revolving around the Sun on a circular orbit with radius 4.2 times the radius of the Earth's orbit around the Sun (which is about 149.6 million kilometers) .Knowing that it takes the Earth 1 year to complete a revolution,how many years does it take for that asteroid?

What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 10²⁴ kg,radius R = 10⁶ m,and the center-to-center distance between any two planets is 10 R.

An imaginary planet has a mass of 8.00 * 10²³ kg and a diameter of 5.0 * 10⁶ m.What is the escape speed from the surface of this planet?

The figure shows a system of three masses.What is the magnitude of the gravitational force on the 10-kg mass? The center-to-center distances between masses are shown in the diagram.

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 * 10⁸ m/s) .What is the radius of a 24 solar mass black hole?

A 51-kg satellite is put into orbit and has 152 MJ of kinetic energy.How high above the Earth's surface is the orbit?

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

The radius of the orbit of a planet around a star is proportional to

Two satellites A and B orbit the Earth with the orbital radius of A,R_A equal to twice that of B,R_A = 2R_B.What is the ratio of their masses M_A/M_B?

A plumb bob located at latitude 63.0^$\circ$ north hangs motionlessly with respect to the ground beneath it.Determine the angle that the string supporting the bob makes with respect to a straight line going through the bob and the center of the Earth.

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the equator.

The distance between Earth and the Sun is 149.6 million km,and the distance between Venus and the Sun is 108.2 million km.How long does it take Venus to orbit once around the Sun?

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the north pole.

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

If the Earth became 5% bigger in radius (R = 1.05R_E) and 10% bigger in mass (M = 1.1M_E) ,about what would the new value of the acceleration of gravity be near the surface of the Earth?

Exam 12: Gravitation

An asteroid has been discovered revolving around the Sun on a circular orbit with radius 4.2 times the radius of the Earth's orbit around the Sun (which is about 149.6 million kilometers) .Knowing that it takes the Earth 1 year to complete a revolution,how many years does it take for that asteroid?

What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 1024 kg,radius R = 106 m,and the center-to-center distance between any two planets is 10 R.

An imaginary planet has a mass of 8.00 * 1023 kg and a diameter of 5.0 * 106 m.What is the escape speed from the surface of this planet?

The figure shows a system of three masses.What is the magnitude of the gravitational force on the 10-kg mass? The center-to-center distances between masses are shown in the diagram.

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 * 108 m/s) .What is the radius of a 24 solar mass black hole?

A 51-kg satellite is put into orbit and has 152 MJ of kinetic energy.How high above the Earth's surface is the orbit?

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

Given the mean distance between the Moon and the Earth is 3.84 * 108 m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 1022 kg on a 70-kg man standing on the surface of the Earth.

The radius of the orbit of a planet around a star is proportional to

Two satellites A and B orbit the Earth with the orbital radius of A,RA equal to twice that of B,RA = 2RB.What is the ratio of their masses MA/MB?

A plumb bob located at latitude 63.0 ∘\circ∘ north hangs motionlessly with respect to the ground beneath it.Determine the angle that the string supporting the bob makes with respect to a straight line going through the bob and the center of the Earth.

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the equator.

The distance between Earth and the Sun is 149.6 million km,and the distance between Venus and the Sun is 108.2 million km.How long does it take Venus to orbit once around the Sun?

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the north pole.

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 1024 kg and its radius is 6.37 * 106 m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

An artificial satellite of 104 kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

If the Earth became 5% bigger in radius (R = 1.05RE) and 10% bigger in mass (M = 1.1ME) ,about what would the new value of the acceleration of gravity be near the surface of the Earth?

What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 10²⁴ kg,radius R = 10⁶ m,and the center-to-center distance between any two planets is 10 R.

An imaginary planet has a mass of 8.00 * 10²³ kg and a diameter of 5.0 * 10⁶ m.What is the escape speed from the surface of this planet?

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 * 10⁸ m/s) .What is the radius of a 24 solar mass black hole?

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

Two satellites A and B orbit the Earth with the orbital radius of A,R_A equal to twice that of B,R_A = 2R_B.What is the ratio of their masses M_A/M_B?

A plumb bob located at latitude 63.0^$\circ$ north hangs motionlessly with respect to the ground beneath it.Determine the angle that the string supporting the bob makes with respect to a straight line going through the bob and the center of the Earth.

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

If the Earth became 5% bigger in radius (R = 1.05R_E) and 10% bigger in mass (M = 1.1M_E) ,about what would the new value of the acceleration of gravity be near the surface of the Earth?