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32. A bead of mass moves along a fixed vertical circle of radius 'R'. The bead is attached to highest point of the circle with a light spring of spring constant k'. If o shown in figure is taken as generalised co-ordinate what is lagrangian of the system (Natural length of spring is 2R and gravitation potential energy is taken to be zero at the centre ofcircle). 35 (a) 2mk²6² - 2KR² (1–-cos0) +mgR cos 20 (b) z mk*o* - 2AR (1-cos 0² + mgRcos 20 (c) 2mR-6? - 2KR² (1-cose)* + mgR cos 20 (d) mr*o² - 2AR² (1- coso) + mgRcos20 TA

32. A bead of mass moves along a fixed vertical circle of radius 'R'. The bead is attached to highest point of the circle with a light spring of spring constant k'. If o shown in figure is taken as generalised co-ordinate what is lagrangian of the system (Natural length of spring is 2R and gravitation potential energy is taken to be zero at the centre ofcircle). 35 (a) 2mk²6² - 2KR² (1–-cos0) +mgR cos 20 (b) z mk*o* - 2AR (1-cos 0² + mgRcos 20 (c) 2mR-6? - 2KR² (1-cose)* + mgR cos 20 (d) mr*o² - 2AR² (1- coso) + mgRcos20 TA

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A bead of mass moves along a fixed vertical circle of radius 'R'. The bead is attached to highest point of the circle with a light spring of spring constant 'k. If 9 shown in figure is taken as generalised co-ordinate what is lagrangian of the system [Natural length of spring is 2R and gravitation potential energy is taken to be zero at the centre o fcircle]. 32. 35 m (a) 2mR-6? - 2kR² (1-cos0) + mgR cos 20 mR-ö² - 2KR² (1-coso)² + mgRcos 20 (e) 2mR-6² - 2kR? (1-cose) + mgR cos 20 (d) mR-o? - 2kR (1-cos 0) + mgRcos20 In previous question, equation of motion of bead for smal value of 9 is: 33. (a) ö+ 20=0 (b) 6+ R 280 (c) ö+0 =0 (d) ö+ R 4g0 =0 2R TA
Transcribed Image Text:A bead of mass moves along a fixed vertical circle of radius 'R'. The bead is attached to highest point of the circle with a light spring of spring constant 'k. If 9 shown in figure is taken as generalised co-ordinate what is lagrangian of the system [Natural length of spring is 2R and gravitation potential energy is taken to be zero at the centre o fcircle]. 32. 35 m (a) 2mR-6? - 2kR² (1-cos0) + mgR cos 20 mR-ö² - 2KR² (1-coso)² + mgRcos 20 (e) 2mR-6² - 2kR? (1-cose) + mgR cos 20 (d) mR-o? - 2kR (1-cos 0) + mgRcos20 In previous question, equation of motion of bead for smal value of 9 is: 33. (a) ö+ 20=0 (b) 6+ R 280 (c) ö+0 =0 (d) ö+ R 4g0 =0 2R TA
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