SparkNotes: Review of Gravitation: Review Test

1. The planets orbit the sun in:

(A) Ellipses

(B) Circles

(C) Hyperbolas

(D) Parabolas

2. The eccentricity of an ellipse with semimajor axis length 10 meters and semiminor axis length 5 meters is:

(A) 1 meter

(B) 0.75 meters

(C) 0.25 meters

(D) 0 meters

3. A planet sweeps out an area equal to half the total area of its orbit in 180 days. Its orbital period is:

(A) 180 days

(B) 240 days

(C) 360 days

(D) Impossible to tell.

4. If the circular orbit of a planet is reduced in radius to 1/8 th of its original value, its period is now, what fraction of its old period, T_old?

(A) 1/5T_old

(B) 1/4T_old

(C) 1/9T_old

(D) 1/8T_old

5. Which is the following orbits are possible around the earth:

Various orbits around the earth.

(A) I, II and III

(B) II, III and not I

(C) I and II, but not III

(D) None of these

6. An eccentricity of zero means the orbit is:

(A) A circle

(B) An ellipse

(C) A hyperbola

(D) A parabola

7. An eccentricity of 1.5 means the orbit is:

(A) A circle

(B) An ellipse

(C) A hyperbola

(D) A parabola

8. If a satellite is orbiting the earth at radius 6×10⁶ meters above the center of the earth. What is its period? (The mass of the earth is 5.98×10²⁴ kilograms).

(A) 2.3×10⁶ secs

(B) 9.3×10⁶ secs

(C) 7.8×10⁶ secs

(D) 4.6×10⁶ secs

9. Kepler's Second Law is an expression of:

(A) Conservation of energy

(B) Conservation of momentum

(C) Conservation of angular momentum

(D) None of these

10. The direction of the force due to gravity between two point objects located at

and

is given by:

(A)

(B)

(C)

-

(D)

-

11. g equals:

(A)

(B)

(C)

(D)

12. The gravitational force that a spherical shell of mass 102 kilograms exerts on a 5 kilogram mass at its center is:

(A) 5.5×10² Newtons

(B) 3.74×10^-8 Newtons

(C) 5.5×10^-8 Newtons

(D) 0

13. If you can throw a ball 10 meters into the air on earth, approximately how high would you me able to throw it on the moon (mass of the moon is 7.35×10²² kilograms and its radius is 1700 kilometers).

(A) 10 meters

(B) 60 meters

(C) 20 meters

(D) Cannot tell from given information.

14. A planet of mass 6×10²⁵ kilograms, orbiting the sun (mass = 1.99×10³⁰ kilograms) has a velocity of 50 kilometers/sec. What is its rate of change of angular momentum at this point:

(A) 1.2×10¹⁰ kgm²/sec

(B) 1.2 ×10⁸ kgm²/sec

(C) 9.3×10^-2 kgm²/sec

(D) 0

15. The correct ordering of the forces in terms of their relative strength, beginning with the strongest is: I) Gravity II) Strong Nuclear Force III) Electromagnetic Force IV) Weak Nuclear Force.

(A) III, I, II, IV

(B) I, III, IV, II

(C) II, IV, III, I

(D) II, III, IV, I

16. A particle of mass 2 kilograms orbits the sun (mass = 1.99×10³⁰) parabolically. Its velocity very far away from the sun is:

(A) 0

(B) 2.4×10¹⁵ m/s

(C) 2.4×10³⁰ m/s

(D) Insufficient information

17. Two stars of equal mass exert a gravitational force on one another. This will cause them to:

(A) Move directly towards one another

(B) One to move in a circle with the other at its center

(C) Both to move in a circle about their center of mass

(D) Cannot tell without knowing their total energy

18. If it is desirable to give a rocket the maximum tangential velocity on its launch, then the best launch site would be:

(A) One of the poles

(B) On the equator

(C) Cape Canaveral

(D) It doesn't matter

19. The total energy of a circular orbit is:

(A)

(B)

(C)

(D)

20. Which of these can not be deduced from Kepler's Laws: I) orbits may be circular, II) The force between two planets goes as 1/r², III) Gravity is a conservative force.

(A) II and III

(B) I only

(C) II only

(D) I and III only

21. Which of the following has the smallest escape velocity:

(A) The sun (mass = 1.99×10³⁰ kilograms, radius = 6.96×10⁸ meters).

(B) Mercury (mass = 3.3×10²⁴ kilograms, radius = 5.4×10⁶ meters).

(C) The moon (mass = 7.35×10²² kilograms, radius = 3.4×10⁶ meters).

(D) The earth (mass = 5.98×10²⁴ kilograms, radius = 6.38×10⁶ meters).

22. The gravitational potential energy of a mass 100 kilometers from the earth, compared to the same mass at the surface is:

(A) Higher and positive

(B) Higher and negative

(C) Lower and positive

(D) Lower and negative

23. The gravitational potential at a point 100 kilometers above the earth's surface is:

(A) 9.8×10^-6 J/kg

(B) -9.8×10^-6 J/kg

(C) 4.9×10^-6 J/kg

(D) -4.9×10^-6 J/kg

24. The units of G are:

(A) Newtons

(B) Nm/kg²

(C) Nm²kg^-1

(D) Nm²/kg²

25. Put these orbits in order of increasing energy: I) parabola II)cicle III) hyperbola IV) ellipse

(A) IV, II, I, III

(B) II, IV, I, III

(C) III, I, IV, II

(D) I, III, IV, II

26. The only orbit to have a positive total energy is:

(A) Parabolic

(B) Circular

(C) Hyperbolic

(D) Elliptical

27. A satellite in low-earth orbit (r

r_e), has a period of:

(A) 22.5 minutes

(B) 2440 minutes

(C) 1 day

(D) 84.5 minutes

28. The tides are caused by which of the following: I) The moon II) The sun III) The rotation of the earth.

(A) II and III only

(B) I and II only

(C) I only

(D) I, II and III

29. The escape velocity from the earth is approximately (mass of the earth is 5.98×10²⁴ kilograms and its radius is 6.38×10⁶ meters):

(A) 11.2 m/sec

(B) 11.2 kilometers/sec

(C) 9.8 kilometers/sec

(D) 5.6 kilometers/sec

30. I) Newton, II)Einstein, III) Copernicus, IV) Kepler. The correct order in which these scientists lived is:

(A) IV, III, II, I

(B) IV, III, I, II

(C) III, IV, I, II

(D) III, I, IV, II

31. Which is true of the gravitational force between the earth and the moon is: I) equal and opposite II) zero at some point between the two.

(A) Both I and II

(B) I only

(C) II only

(D) Neither correct

32. The minimum radius of orbit for a planet with ε = 0.75 is:

(A)

(B)

(C)

(D)

33. What is the semimajor axis length of an elliptical earth orbit with apogee 1.4×10⁷ meters and perigee 1.2×10⁷ meters?

(A) 1.4×10⁷ meters

(B) 1.3×10⁷ meters

(C) 1.2×10⁷ meters

(D) 2.6×10⁷ meters

34. The gravitational force between two objects is: I) Conservative II) Independent of intervening objects III) Central.

(A) I only

(B) II only

(C) III only

(D) None of the above

35.

Gravitational field between two masses

In the arrangement shown in Figure A.2, a mass exactly half way between the two masses shown would have a gravitational potential energy of:

(A)

(B)

(C)

(D) 0

36. A planet in an elliptical orbit travels fastest at its:

(A) Aphelion

(B) Perihelion

(C) Focus

(D) Cannot tell

37. An experiment to determine G was successfully performed by:

(A) Newton

(B) Kepler

(C) Cavendish

(D) Rayleigh

38. Which of these is an expression of angular momentum: I)

×

II)

mvr sinθ III)

1/2×rv sinθ.

(A) I only

(B) II only

(C) I and III only

(D) I and II only

39. Escape velocity depends on:

(A) Speed and direction of launch.

(B) Speed of launch, but not direction.

(C) Direction of launch, but not speed.

(D) Neither speed nor direction of launch.

40. The total energy of Io, orbiting Jupiter at a distance of 4.22×10⁶ meters is (mass of Jupiter is 1.9 ×10²⁷ kilograms, mass of Io is 8.9×10²² kilograms):

(A) 1.34×10³⁴ J

(B) 2.68×10³⁴ J

(C) -2.68×10³⁴ J

(D) -1.34×10³⁴ J

41. Which of the following is an expression of the principle of equivalence?

(A) F = m_ia

(B) m_g = m_i

(C) mg =

(D) None of these

42. To which of the following could Kepler's Laws be applied? I) a comet, II) a binary star system, III) a projectile on the earth.

(A) II only

(B) II and III only

(C) I and II only

(D) All of these

43. The gravitational potential energy can be defined as:

(A)

-

.d

(B)

-

.d

(C) -

-

.d

(D) -

-

.d

44. For a circular orbit, which of the following is true for the kinetic energy, T?

(A) T = 1/2| U|

(B) T = | U|

(C) T = 1/2| E|

(D) T = - 1/2| E|

45. An 80 kilogram astronaut is in a spaceship accelerating upwards 4.9 m/s² far away from any star or planet. His apparent weight as measured by some scales in the spaceship would be:

(A) 80 kilograms

(B) 40 kilograms

(C) 160 kilograms

(D) 0

46. Assuming the earth is in a circular orbit about the sun, what is the speed of the earth (the mass of the sun is 1.99×10³⁰ kilograms and the earth- sun distance is 150×10⁹ meters).

(A) 8.8×10⁸ m/s

(B) 1.5×10⁴ m/s

(C) 3.0×10⁴ m/s

(D) 17.6×10⁸ m/s

47. If the ratio of a planet's perihelion distance to aphelion distance is 0.75, then the ratio of its greatest to least velocity on its orbit is:

(A) 0.75

(B) 1.5

(C) 2.5

(D) 1.33

48. If the orbits of Venus and the Earth are both circular, with the period of the earth orbit 1 year and the period of Venus, 0.615 days, what is the ratio of the earth's orbit to Venus's orbit?

(A) 1.38

(B) 1.63

(C) 2.64

(D) 4.30

49. The correct ordering, in terms of increasing numerical value of the kinetic, potential and total energies for a circular orbit is:

(A) Kinetic, total, potential

(B) Total, kinetic, potential

(C) Potential, total, kinetic

(D) Depends on the radius of the orbit

50. A binary star system has two stars of masses m₁ and m₂, orbiting about their common center of mass with radii r₁ and r₂ respectively. What is the square of the period of their orbit?

(A)

(B)

(C)

(D)