Physics - W.E.P. Question with Solution | TestHub
A bead slides on a fixed frictionless wire bent into a horizontal semicircle of radius as shown in figure. In addition to any normal forces exerted by the wire, the bead is subjected to an external force that points directly away from origin and depends on distance r from the origin according to the formula
Options:(select one or more)
Answer:
Solution:
The force points along r-hat with magnitude depending only on r, so it is a central force (A true), and every such central force is conservative (B true). The bead starts at the origin (r = 0) and leaves the wire at the far end of the diameter (r = 2R0). Work done by it: integral of F0 (r/R0)^2 dr from 0 to 2R0 = (F0/R0^2)(8 R0^3 / 3) = 8 F0 R0 / 3 (C true). Speed on leaving: v = sqrt(v0^2 + 2W/m) = sqrt(v0^2 + 16 F0 R0 / 3m); option D writes 18 instead of 16, so D is false. Answer: A, B, C.
