Classical Mechanics-System of Particles (IFS (Forests Services) Physics (Mains)): Questions 1 - 4 of 4

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Question number: 1

» Classical Mechanics » System of Particles » Generalised Coordinates and Momenta

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Appeared in Year: 2012

Essay Question▾

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Using D’ Alembert’s principle, show that the following relation can be obtained for a system of particles under generalized coordinates,

What is the significance of ? (Paper-1) (section – A)

Explanation

  • The mathematical statement of D’ Alembert’s principle is given as,
  • Transform D’ Alembert’s principle into expressions containing independent generalized coordinates only.

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Question number: 2

» Classical Mechanics » System of Particles » Cyclic Coordinates

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Appeared in Year: 2012

Short Answer Question▾

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Express Lagrange’s equation of motion for the cyclic coordinate and show that the result leads to the general conservation theorem for the generalized momentum coordinates. (Paper - 1) (Section – A)

Question number: 3

» Classical Mechanics » System of Particles » Generalised Coordinates and Momenta

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Appeared in Year: 2012

Essay Question▾

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Starting with Newton’s second law of motion, establish D’ Alembert’s principle and discuss its significance? (Paper-1) (Section –A)

Explanation

  • Let consider a system described by generalized coordinates . And this system undergoes a certain displacement in configuration space. If for this displacement it does not take any time and it is consistent with the constraints on the system. This kind of displacement is called virtual

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Question number: 4

» Classical Mechanics » System of Particles » Constraints

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Appeared in Year: 2010

Essay Question▾

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How can one introduce the constraints of motion through the concept of generalized coordinate systems? Write down the set of transformation equations for a system of particles relating the generalized coordinates with real coordinates. (Section A)

Explanation

  • In mechanics, mostly problems can be reduced by solving differential equation, which consist of all the forces acting on a system. A such equation is given by,

  • As we know, all mechanical systems have constraint force acting on them to some degree. A constrain

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