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Phys-301-121 Set-VI [This problem set is due by Saturday, the 17th Muharram, 1434 at 4.00 p.m.] Instructions: Please solve all problems completely and clearly [state your assumptions]. If you do not understand the question(s) please call me. Let’s start: بسم هللا Please solve this problem set independent of other live beings (no colleagues, friends, forums or instructors) Question-1: Using variational calculus, show that the short path between two points on a sphere is that which treks an arc of its great circle that joins these two points. Question 2: Solve M&T 6.8-a Question 3: A small object is placed on top of a spherical shell of radius R. It is slightly displaced and the object slides without friction on top of the shell. a. Use Newtonian mechanics to find the angle at which the object is no longer in contact with the sphere. b. Use Lagrange mechanics (with undetermined multipliers) to find the angle at which the object is no longer in contact with the sphere. Question 4: Solve M&T 7.3