An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 106 m, R = 5.0 106 m, and M = 4.0 1024 kg.
a. 7.8 km/s
b. 3.5 km/s
c. 5.4 km/s
d. 6.9 km/s
e. 4.8 km/s
[Ques. 2] What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 106 m around the Earth? (Mass of Earth = 6.0 1024 kg.)
a. 5.0 109 J
b. 1.0 1010 J
c. 1.5 1010 J
d. 2.0 1010 J
e. 2.5 109 J
[Ques. 3] A spacecraft (mass = m1) orbits a planet (mass = m2) in a circular orbit (radius = r). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?
a. Gm1m2/(4r)
b. Gm1m2/R
c. Gm1m2/(2R)
d. Gm1m2/(3R)
e. 2Gm1m2/(5R)
[Ques. 4] A spaceship of mass m1 circles a planet (mass = m2) in an orbit of radius r. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?
a. Gm1m2/(2r)
b. Gm1m2/(3r)
c. Gm1m2/(4r)
d. Gm1m2/(6r)
e. 3Gm1m2/(4r)
[Ques. 5] 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. 88 N
b. 55 N
c. 36 N
d. 98 N
e. 18 N
[Ques. 6] A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible. Which of the following statements is true?
a. There is only one force acting on the satellite.
b. There are two forces acting on the satellite, and their resultant is zero.
c. There are two forces acting on the satellite, and their resultant is not zero.
d. There are three forces acting on the satellite.
e. None of the preceding statements are correct.
[Ques. 7] What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?
a. 4.8 m/s2
b. 1.1 m/s2
c. 3.3 m/s2
d. 2.5 m/s2
e. 6.5 m/s2
[Ques. 8] 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.
a. 0.41 D
b. 0.33 D
c. 0.37 D
d. 0.29 D
e. 0.14 D
[Ques. 9] A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 106 m. What is the magnitude of the gravitational force on the satellite by planet Cruton?
a. 63 N
b. 58 N
c. 68 N
d. 73 N
e. 50 N
[Ques. 10] The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 106 m. What is the mass of planet Nutron?
a. 6.2 1028 kg
b. 5.0 1028 kg
c. 5.5 1028 kg
d. 4.3 1028 kg
e. 3.7 1028 kg
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