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# 10222_01%20exam%20answers - PHS 1022 Paper 2 2001...

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V:\office\1022\Solutions\10222_01 exam answers.doc p.1 27/10/2006 PHS 1022 Paper 2 2001 Examination (Rot & Grav Mechanics, Quantum) Answers 2006 Note: several topics are no longer on the syllabus. Students should consider only questions nominated by staff or which obviously relate to the current syllabus. SECTION A Question A1 (a) 2 × ml 2 (b) 4 3 2 2 2 2 2 l l l d y x = = 4 7 4 3 2 2 2 2 2 ml l m l m = + × (c) ω = 2 π × 5 rad s -1 (i) J π ml I ω K 2 2 2 100 2 1 = = (ii) J π ml K 2 2 100 8 7 = Question A2 (a) v = r ω (b) K f = mgh = ½ I ω 2 + ½ mv 2 1 2 2 2 2 2 2 548 0 300 0 32 0 120 50 9 1 8 9 20 1 2 1 2 2 = = × + × × = + = + = ms . v s m . ) . ( . . . mr I gh m r I mgh v (c) ½ mv 2 = ½ × 0.12 × (0.548) 2 = 1.8 × 10 -2 J (d) ω = v/r = 171 rad s -1 (e) ½ I ω 2 = 1.39 J (for interest, mgh = 1.41 J ) Question A3 (a) T , L J L + ) L ) L L T p ) t

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V:\office\1022\Solutions\10222_01 exam answers.doc p.2 27/10/2006 (b) Question A4 (a) 2 R GM (b) The gravity field only depends on the mass contained within the sphere of radius R /2. Since there is spherical symmetry a g is the same at all points on the sphere of r = R /2. (c) (ii) remain the same since this extra mass is outside R /2 and spherically symmetrical. Question A5 (a) (b) 1 2 2 56 1 2 60 900 2 0 6 0 8 9 1 1 : diagram hand right From and : equation Key = × × × = = = = = = = s rad . π ) . ( . . Mgd ω Mr i τ L t L L ω t ω L L mgd τ τ dt dL p p () () 2 3 2 2 2 2 8 1 2 Since 2 R GM a , R R M M R GM a g g = = = = g total g U r GMm U K E r GMm U r GMm mv K 2 1 2 1 2 1 2 1 2 2 = = + = = = = 1 2 6 11 24 11200 2 2 1 10 38 . 6 10 67 . 6 10 98 . 5 ) ( = = = = × × × × = = ms m U v ) (R U mv K J m R m GM R U g esc e g esc e e e g
V:\office\1022\Solutions\10222_01 exam answers.doc p.3 27/10/2006 (c) 2 2 r GMm r mv = 1 3 6 6 24 11 10 70 7 10 35 0 10 38 6 10 98 5 10 67 6 × = × + × × × × = = ms . . . . . r GM v SECTION B - QUANTUM Question B1 (a) Equate the dissociation energy of a AgBr molecule (0.68 eV) with the energy of the photon i.e. nm or m . J . . ) ms

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10222_01%20exam%20answers - PHS 1022 Paper 2 2001...

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