Three identical stars, each of mass M, form an equilateral triangle (stars$$ are positioned at the $$corners) that rotates around the centre of the triangle. The system is isolated and edge length of triangle is ‘L’. The minimum amount of work done that is required to dismantle the system is (Assume$$ L is much greater than size of $$stars)

Question

Three identical stars, each of mass  M, form an equilateral triangle (stars$$ are positioned at the $$corners) that rotates around the centre of the triangle. The system is isolated and edge length of triangle is ‘L’. The minimum amount of work done that is required to dismantle the system is (Assume$$ L is much greater than size of $$stars)

Infinity Learn · Accepted Answer

Given mass of each $$star=$$ MLength of triangle  $$=LTotal$$ energy of system initially $$=$$$$KE$$$$+$$$$PE$$ $$PE$$$$=$$−$$3GM2LKE=312MV2$$ Where  $$MV2R=2GM2L2cos300=3GM2L2$$& $$R=L3$$∴$$KE$$$$=312MV2=32$$×$$GM2LHence$$,  $$TEi=$$−$$3GM2L+3GM22L=$$−$$32GM2L$$ $$TEf=0$$ Work done $$=$$ TEf−$$TEi=32GM2L$$

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