Page 1 of 9 CTGravity-1. Two spherical masses m and M are a distance r apart. The distance between their centers is halved (decreased by a factor of 2). What happens to the magnitude of the force of gravity between them? The force increases by a factor of A) 2 B) 2 C) 22 D) 4 E) 8 Answer: 4 CTGravity-2. At a particular instant, two asteroids in inter-galactic space are a distance r = 20 km apart. Asteroid 2 has 10 times the mass of asteroid 1. The magnitudes of the accelerations of asteroids 1 and 2 are a1 and a2, respectively. What is the ratio 21aa ? A) 10 B) 1/10 C) 1 D) cannot be determined. Answer: 10 Each mass feels the same sized force. The smaller mass has the bigger acceleration. CTGravity-3. Planet X has the same mass as the Earth, but 1/2 the radius. (Planet X is more dense than Earth). What is the acceleration of gravity on Planet X? A) gE (same as Earth) B) 2 gE C) 4 gE D) 8 gE E ) None of these. Answer: 4 gE r m1 m2 = 10 m1 r m MPage 2 of 9 CTGravity-4. A satellite is in circular orbit at an altitude of 100 miles above the surface of the Earth. The satellite’s pre-launch weight is its weight measured on the ground. The magnitude of the force of gravity on the satellite while it is in orbit is.. A) slightly greater than its pre-launch weight. B) the same as its pre-launch weight. C) slightly less than its pre-launch weight. D) much less than its pre-launch weight, but not zero. E) zero. Answer: slightly less than its pre-launch weight. The satellite is only slightly further from the center of the earth when it is in orbit, compared to when it is on the ground. CTGravity-5. Two satellites, A and B, are in circular orbit around the earth. The distance of satellite B from the center of the Earth is twice that of satellite A. What is the ratio of the magnitudes of the accelerations of A to B? ABaa .... A) 1 B) 2 C) 4 D) 1/2 E) 1/4 Answer: 4 A B EarthPage 3 of 9 CTGravity-6. A rock is released from rest at a point in space far from Earth, beyond the orbit of the Moon. The rock falls toward the Earth and crosses the orbit of the Moon. When the rock is the same distance from the Earth as the Moon, the magnitude of the acceleration of the rock is .. (Ignore the gravitational force between the rock and the Moon.) A) greater B) smaller C) the same as the acceleration of the Moon. Answer: the same as The acceleration of gravity depends only the distance to the center of the earth. As the rock falls toward the Earth, its acceleration is.. (neglect Moon’s gravity) A) constant. B) not constant. Answer: not constant, as the rock gets closer to Earth, the acceleration of gravity increases CTGravity-7. At time t=0, a satellite in circular orbit about the Earth is directly over Denver, 300 miles above the city, and traveling eastward at 16,000 mph. At the same time, a rock is released from rest 300 miles above the city, very near the satellite. True or False: at t=0+, the accelerations of the rock and the satellite are identical. A) True B) False Answer: True Earth Moon rock Denver rock satellitePage 4 of 9 CTGravity-8. Suppose the Earth had no atmosphere and a projectile was fired from a mountain top with sufficient speed to put it in circular orbit. The magnitude of the acceleration of the projectile while in orbit would be.. A) much less than g (because it doesn't fall to the ground) B) much greater than g C) approximately g D) Impossible to tell. Answer: approximately g CTGravity-9. Kepler's third law states that the ratio 32rT is a constant for all the planets. The period T of the Earth is 1 year. An astronomical unit (1 A.U.) is defined as the mean distance from the Earth to the Sun, therefore the mean Earth-Sun distance is 1A.U. Consider an asteroid in circular orbit around the Sun with radius r = 2A.U. The period of the asteroid is.. A) 2 years. B) 3 years C) 23/2 2.83 years. D) 22/3 1.59 years E) None of these. Answer: 23/2 2.83 years. For the earth, T = 1 year and r = 1AU. So using units of years for time, and units of AU for distance, T2/r3 = 12/13 = 1 yr2/AU3 for the earth. But T2/r3 = the same constant (1 yr2/AU3) for all objects orbiting the sun. So for the asteroid T2/r3 = 1, T = (r3)1/2 = r3/2 = 23/2 yearsPage 5 of 9 CTGravity-10. A planet in elliptical orbit around a star moves from the point in its orbit furthest from the star (A) to the closest point (P). The work done by the force of gravity during this movement is: A) zero B) positive C) negative. Answer: positive The planet executes one complete orbit starting from point A and returning to A. The work done by the force of gravity during this orbit is: A) zero B) Positive C) Negative. Answer: zero CTGravity-11. The gravitational PE, U(r) = GMm/r of a two mass system (m << M) is plotted. Mass M is stationary at the origin and mass m is at r = r0 . Also shown is the total energy Etot . Which arrow represents the KE of mass m? A B C D) none of these Answer: A KE + PE = Etot A P r U(r) Etot r0 A B CPage 6 of 9 CTGravity-12. A projectile is fired from an airless world with a speed = vescape. What is the total energy (Etot = KE – GMm/r ) of the projectile? A) Etot = 0 B) Etot < 0 C) Etot > 0 Answer: Etot = 0 CTGravity-13.Does escape speed depend on launch angle? That is, if a projectile is given an initial speed vo, is it more likely to escape an (airless) planet, if fired straight up than if fired at an angle? A) Yes B) No Answer: No. The escape speed is independent of angle. CTGravity-14. A planet is in elliptical orbit around the Sun. The zero of potential energy U is chosen at r = , so U rGMmr( ) . How does the magnitude of U UUcompare to the KE? A) | U | > KE B) | U | < KE C) | U | =KE D) depends on the position in the orbit. Answer: | U | > KE Since Etot < 0 (bound orbit), the negative U must be larger in magnitude than the positive KE.Page 7 of 9 CTGravity-15. Suppose a projectile is fired straight upward from the surface of an airless planet of radius R with the escape velocity vesc (meaning the projectile will just barely escape the planet's gravity -- it will asymptotically approach infinite distance and zero speed.) What is the projectile's speed when it is a distance 4R from …
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