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A particle in a cyclotron travels in a circle of 2000m radius. What is the difference in magnitude of its
displacement (a chord) and its distance of traveled (an arc) in one fourth sliced on the circular path or
the circle?

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Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 6.9 ✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar masses
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Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. a) What should the orbital period of that star be in years? b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
Suppose you could pack neutrons (mass = 1.67 × 10-27 kg) inside a small ball of radius 0.026 m in the same way as neutrons and protons are packed together in the nucleus of an atom. (a) Approximately how many neutrons would fit inside the ball? (b) A small object is placed 3.7 m from the center of the neutron-packed ball, and the ball exerts a gravitational force on it. When the object is released, what is the magnitude of the acceleration that it experiences? Ignore the gravitational force exerted on the object by the earth.
What value is the acceleration of 45 microns/min2 in the units of nm per seconds squared?