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Review of Gravitation
Physics
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1. The planets orbit the sun in:
Ellipses
Circles
Hyperbolas
Parabolas
2. The eccentricity of an ellipse with semimajor axis length 10 meters and semiminor axis length 5 meters is:
1 meter
0.75 meters
0.25 meters
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:
180 days
240 days
360 days
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}
?
1/5
T
_{old}
1/4
T
_{old}
1/9
T
_{old}
1/8
T
_{old}
5. Which is the following orbits are possible around the earth:
Various orbits around the earth.
I, II and III
II, III and not I
I and II, but not III
None of these
6. An eccentricity of zero means the orbit is:
A circle
An ellipse
A hyperbola
A parabola
7. An eccentricity of 1.5 means the orbit is:
A circle
An ellipse
A hyperbola
A parabola
8. If a satellite is orbiting the earth at radius
6×10
^{6}
meters above the center of the earth. What is its period? (The mass of the earth is
5.98×10
^{24}
kilograms).
2.3×10
^{6}
secs
9.3×10
^{6}
secs
7.8×10
^{6}
secs
4.6×10
^{6}
secs
9. Kepler's Second Law is an expression of:
Conservation of energy
Conservation of momentum
Conservation of angular momentum
None of these
10. The direction of the force due to gravity between two point objects located at
and
is given by:


11.
g
equals:
12. The gravitational force that a spherical shell of mass 102 kilograms exerts on a 5 kilogram mass at its center is:
5.5×10
^{2}
Newtons
3.74×10
^{8}
Newtons
5.5×10
^{8}
Newtons
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
7.35×10
^{22}
kilograms and its radius is
1700
kilometers).
10 meters
60 meters
20 meters
Cannot tell from given information.
14. A planet of mass
6×10
^{25}
kilograms, orbiting the sun (mass
= 1.99×10
^{30}
kilograms) has a velocity of 50 kilometers/sec. What is its rate of change of angular momentum at this point:
1.2×10
^{10}
kgm
^{2}
/sec
1.2
×10
^{8}
kgm
^{2}
/sec
9.3×10
^{2}
kgm
^{2}
/sec
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.
III, I, II, IV
I, III, IV, II
II, IV, III, I
II, III, IV, I
16. A particle of mass 2 kilograms orbits the sun (mass
= 1.99×10
^{30}
) parabolically. Its velocity very far away from the sun is:
0
2.4×10
^{15}
m/s
2.4×10
^{30}
m/s
Insufficient information
17. Two stars of equal mass exert a gravitational force on one another. This will cause them to:
Move directly towards one another
One to move in a circle with the other at its center
Both to move in a circle about their center of mass
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:
One of the poles
On the equator
Cape Canaveral
It doesn't matter
19. The total energy of a circular orbit is:
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/
r
^{2}
, III) Gravity is a conservative force.
II and III
I only
II only
I and III only
21. Which of the following has the smallest escape velocity:
The sun (mass
= 1.99×10
^{30}
kilograms, radius
= 6.96×10
^{8}
meters).
Mercury (mass
= 3.3×10
^{24}
kilograms, radius
= 5.4×10
^{6}
meters).
The moon (mass
= 7.35×10
^{22}
kilograms, radius
= 3.4×10
^{6}
meters).
The earth (mass
= 5.98×10
^{24}
kilograms, radius
= 6.38×10
^{6}
meters).
22. The gravitational potential energy of a mass 100 kilometers from the earth, compared to the same mass at the surface is:
Higher and positive
Higher and negative
Lower and positive
Lower and negative
23. The gravitational potential at a point 100 kilometers above the earth's surface is:
9.8×10
^{6}
J/kg
9.8×10
^{6}
J/kg
4.9×10
^{6}
J/kg
4.9×10
^{6}
J/kg
24. The units of
G
are:
Newtons
Nm/kg
^{2}
Nm
^{2}
kg
^{1}
Nm
^{2}
/kg
^{2}
25. Put these orbits in order of increasing energy: I) parabola II)cicle III) hyperbola IV) ellipse
IV, II, I, III
II, IV, I, III
III, I, IV, II
I, III, IV, II
26. The only orbit to have a positive total energy is:
Parabolic
Circular
Hyperbolic
Elliptical
27. A satellite in lowearth orbit (
r
r
_{e}
), has a period of:
22.5 minutes
2440 minutes
1 day
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.
II and III only
I and II only
I only
I, II and III
29. The escape velocity from the earth is approximately (mass of the earth is
5.98×10
^{24}
kilograms and its radius is
6.38×10
^{6}
meters):
11.2 m/sec
11.2 kilometers/sec
9.8 kilometers/sec
5.6 kilometers/sec
30. I) Newton, II)Einstein, III) Copernicus, IV) Kepler. The correct order in which these scientists lived is:
IV, III, II, I
IV, III, I, II
III, IV, I, II
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.
Both I and II
I only
II only
Neither correct
32. The minimum radius of orbit for a planet with
ε
= 0.75
is:
33. What is the semimajor axis length of an elliptical earth orbit with apogee
1.4×10
^{7}
meters and perigee
1.2×10
^{7}
meters?
1.4×10
^{7}
meters
1.3×10
^{7}
meters
1.2×10
^{7}
meters
2.6×10
^{7}
meters
34. The gravitational force between two objects is: I) Conservative II) Independent of intervening objects III) Central.
I only
II only
III only
None of the above
35.
Gravitational field between two masses
In the arrangement shown in , a mass exactly half way between the two masses shown would have a gravitational potential energy of:
0
36. A planet in an elliptical orbit travels fastest at its:
Aphelion
Perihelion
Focus
Cannot tell
37. An experiment to determine
G
was successfully performed by:
Newton
Kepler
Cavendish
Rayleigh
38. Which of these is an expression of angular momentum: I)
×
II)
mvr
sin
θ
III)
1/2×
rv
sin
θ
.
I only
II only
I and III only
I and II only
39. Escape velocity depends on:
Speed and direction of launch.
Speed of launch, but not direction.
Direction of launch, but not speed.
Neither speed nor direction of launch.
40. The total energy of Io, orbiting Jupiter at a distance of
4.22×10
^{6}
meters is (mass of Jupiter is 1.9
×10
^{27}
kilograms, mass of Io is
8.9×10
^{22}
kilograms):
1.34×10
^{34}
J
2.68×10
^{34}
J
2.68×10
^{34}
J
1.34×10
^{34}
J
41. Which of the following is an expression of the principle of equivalence?
F
=
m
_{i}
a
m
_{g}
=
m
_{i}
mg
=
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.
II only
II and III only
I and II only
All of these
43. The gravitational potential energy can be defined as:

.
d

.
d


.
d


.
d
44. For a circular orbit, which of the following is true for the kinetic energy, T?
T
= 1/2
U

T
= 
U

T
= 1/2
E

T
=  1/2
E

45. An 80 kilogram astronaut is in a spaceship accelerating upwards 4.9 m/s
^{2}
far away from any star or planet. His apparent weight as measured by some scales in the spaceship would be:
80 kilograms
40 kilograms
160 kilograms
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
1.99×10
^{30}
kilograms and the earth sun distance is
150×10
^{9}
meters).
8.8×10
^{8}
m/s
1.5×10
^{4}
m/s
3.0×10
^{4}
m/s
17.6×10
^{8}
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:
0.75
1.5
2.5
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?
1.38
1.63
2.64
4.30
49. The correct ordering, in terms of increasing numerical value of the kinetic, potential and total energies for a circular orbit is:
Kinetic, total, potential
Total, kinetic, potential
Potential, total, kinetic
Depends on the radius of the orbit
50. A binary star system has two stars of masses
m
_{1}
and
m
_{2}
, orbiting about their common center of mass with radii
r
_{1}
and
r
_{2}
respectively. What is the square of the period of their orbit?
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