I had rather discovered one true face of science than be King of Persia. L-7 Quotation attributed sometimes to Archimedes, quoted by Frederick the Great of Statics-Points Prussia (d. 1786) in reference to himself. 270 Three identical cylinders of radius r are placed inside a hollow cylinder of radius R. All cylinder axes (perpendicular to the paper) are horizontal. There is no friction. The cylinders B and C are on the verge of separating (= infinitesimally separated, as shown). (a) From the statics equations for A and B, show that the angle between the normal under B and the - vertical is given by tan 0 = - (The same result is obtained for A and C, of course, since B 31/3 and C have mirror image forces on them.) (b) By trigonometry of geometry, show that R must be r (1 + 217 )in order for B and C to be on the verge of separating. (Find sin 0 and cos 0 from a triangle; don't find 0.) (Problem from a senior-year high school physics book used in England.) B 1 Two beads of weights w and w can slide with negligible friction on a circular which