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21. A smooth ring of radius R and mass m lies on a frictionless surface. A point mass, also of mass m, is placed just inside the ring and given a speed v tangent to the inner surface of the ring. How long does it take for the point mass to return to its initial position relative to the ring?

21. A smooth ring of radius R and mass m lies on a frictionless surface. A point mass, also of mass m, is placed just inside the ring and given a speed v tangent to the inner surface of the ring. How long does it take for the point mass to return to its initial position relative to the ring?

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21. A smooth ring of radius R and mass m lies on a frictionless surface. A point mass, also of mass m, is placed just inside the ring and given a speed v tangent to the inner surface of the ring. How long does it take for the point mass to return to its initial position relative to the ring? (A) TH √2=R (B) V (C) 2TR ບ m (D) 22. Two springs with different spring constants are connected in three ways, as shown. KA kB kc Q. www. 2√2TR V useit (E) 4TR V In the second case, the springs are connected to opposite ends of a string, which runs under a massless frictionless pulley. In each case, the two springs act like a single spring with an effective spring constant KA, KB, or kc. Which of the following is correct? (A) KA > kB > kc (B) kA> kc> kB (C) kc > kB > kA (D) kc > KA > kB (E) kB > KA> kc 23. An astronomer on Earth, which is a distance Lo from the Sun, observes a star and galaxy. The star is a distance L, » Lo away, and the galaxy is much further away than the star. Throughout the year, the angular distance between the star and galaxy appears to vary, reaching a minimum of 2 arcseconds on January 1st and a maximum of 2.5 arcseconds on July 1st. (One degree is equal to 3600 arcseconds.) Assume the Sun, star, and galaxy do not move relative to each other, and that the Earth's orbit lies
Transcribed Image Text:21. A smooth ring of radius R and mass m lies on a frictionless surface. A point mass, also of mass m, is placed just inside the ring and given a speed v tangent to the inner surface of the ring. How long does it take for the point mass to return to its initial position relative to the ring? (A) TH √2=R (B) V (C) 2TR ບ m (D) 22. Two springs with different spring constants are connected in three ways, as shown. KA kB kc Q. www. 2√2TR V useit (E) 4TR V In the second case, the springs are connected to opposite ends of a string, which runs under a massless frictionless pulley. In each case, the two springs act like a single spring with an effective spring constant KA, KB, or kc. Which of the following is correct? (A) KA > kB > kc (B) kA> kc> kB (C) kc > kB > kA (D) kc > KA > kB (E) kB > KA> kc 23. An astronomer on Earth, which is a distance Lo from the Sun, observes a star and galaxy. The star is a distance L, » Lo away, and the galaxy is much further away than the star. Throughout the year, the angular distance between the star and galaxy appears to vary, reaching a minimum of 2 arcseconds on January 1st and a maximum of 2.5 arcseconds on July 1st. (One degree is equal to 3600 arcseconds.) Assume the Sun, star, and galaxy do not move relative to each other, and that the Earth's orbit lies
within their plane. What is the ratio L₁/Lo? (A) 1.4 x 104 2 arcsecond star galaxy 2.5 arcsecond star (B) 7 x 104 ●galaxy Jan 1st. July 1st (astronomer's view through the telescope) (C) 4 x 105 (D) 8 x 105 (E) 4 x 106
Transcribed Image Text:within their plane. What is the ratio L₁/Lo? (A) 1.4 x 104 2 arcsecond star galaxy 2.5 arcsecond star (B) 7 x 104 ●galaxy Jan 1st. July 1st (astronomer's view through the telescope) (C) 4 x 105 (D) 8 x 105 (E) 4 x 106
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