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PG Exam 2016 : Physics (Banaras Hindu University (BHU), Varanasi )

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics

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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES CLASSICAL MECHANICS SOLUTIONS NET/JRF (JUNE-2011) Q1. A particle of unit mass moves in a potential V x ax 2 b , where a and b are positive x2 constants. The angular frequency of small oscillations about the minimum of the potential is (a) Ans: 8b 8a (b) (c) 8a / b (d) 8b / a (b) 1 V 2b b b 4 Solution: V x ax 2 2 0 2ax 3 0 ax 4 b 0 x0 . x x x a 2V k Since , m 1 and k 2 where xo is stable equilibrium point. x x x m 0 1 2V 6b 6b b 4 Hence k 2 2a 4 2a 8a at x x0 . b x x0 a a Thus 8a . Q2. The acceleration due to gravity (g) on the surface of Earth is approximately 2.6 times that on the surface of Mars. Given that the radius of Mars is about one half the radius of Earth, the ratio of the escape velocity on Earth to that on Mars is approximately (a) 1.1 Ans: (b) 1.3 (c) 2.3 (d) 5.2 (c) Solution: Escape velocity = 2gR ge R e Escape velocity of Earth R g 2.3 where e 2 and e 2.6. Rm gm Escape velocity of Mass gm R m Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1

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