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Exam 12: Gravitation

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Question 31

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A very small round ball is located near a large solid sphere of uniform density. The force that the large sphere exerts on the ball

A) is exactly the same as it would be if all the mass of the sphere were concentrated at the center of the sphere.
B) is approximately the same as it would be if all the mass of the sphere were concentrated at the center of the sphere.
C) is independent of the mass of the ball.
D) is independent of the mass of the sphere.
E) can only be calculated using calculus.

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Question 32

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You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 10⁷ m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.8 × 10¹¹ m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s². What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10^-11 N ∙ m²/kg².)

A) (a) 7.2 kg × 10²⁵ kg, (b) 2.9 kg × 10³⁰ kg
B) (a) 1.3 kg × 10²⁶ kg, (b) 2.9 kg × 10³⁰ kg
C) (a) 7.2 kg × 10²⁵ kg, (b) 1.7 kg × 10³⁰ kg
D) (a) 1.3 kg × 10²⁶ kg, (b) 1.7 kg × 10³⁰ kg

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Question 33

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A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth. If the satellite instead had mass 4m, its orbital period would be

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 × 10^-11 N ∙ m²/kg².

Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to

A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 10²⁴ kg and G = 6.67 × 10^-11 N ∙ m2/kg²)

Planet Z-34 has a mass equal to 1/3 that of Earth, a radius equal to 1/3 that of Earth, and an axial spin rate 1/2 that of Earth. With g representing, as usual, the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

A satellite is in circular orbit at an altitude of 1500 km above the surface of a nonrotating planet with an orbital speed of 9.2 km/s. The minimum speed needed to escape from the surface of the planet is 14.9 km/s, and G = 6.67 × 10^-11 N ∙ m²/kg². The orbital period of the satellite is closest to

A meteoroid, heading straight for Earth, has a speed of 14.8 km/s relative to the center of Earth as it crosses our moon's orbit, a distance of 3.84 × 10⁸ m from the earth's center. What is the meteoroid's speed as it hits the earth? You can neglect the effects of the moon, Earth's atmosphere, and any motion of the earth. (G = 6.67 × 10^-11 N ∙ m²/kg², Mearth = 5.97 × 10²⁴ kg)

An object drops a distance h in a time of 6.3 s on the surface of the earth (neglecting air effects) . How long would it take the same object to drop the same distance on the surface of spherical asteroid X having a mass of 1.1 × 10²² kg and a radius of 4.0 × 10⁵ m? (G = 6.67 × 10^-11 N ∙ m²/kg², Mearth = 5.97 × 10²⁴ kg, Rearth = 6.38 × 10⁶ m)