Classical Mechanics (IFS (Forests Services) Physics (Mains)): Questions 1 - 5 of 7

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Question number: 1

» Classical Mechanics » Particle Dynamics » Conservation of Linear and Angular Momentum

Appeared in Year: 2011

Short Answer Question▾

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A particle of rest mass ‘M’ moving at a velocity ‘u’ collides with a stationary particle of rest mass ‘m’. If the particle stick together, show that the speed of the composite ball is equal to,

Equation Where Equation (Paper-1) (Section –A)

Question number: 2

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

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,

Equation

Equation

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

Explanation

  • The mathematical statement of D’ Alembert’s principle is given as,

Equation

  • Transform D’ Alembert’s principle into expressions containing independent generalized coordinates only.

Equation

  • Equation (2), gives an infinitesimal virtual displacement Equation at particular instant Equation . We can see that the variation with respect to time is absent in equation
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Question number: 3

» Classical Mechanics » System of Particles » Cyclic Coordinates

Appeared in Year: 2012

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

Question number: 4

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

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 Equation generalized coordinates Equation . 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.

  • In virtual

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Question number: 5

» Classical Mechanics » Particle Dynamics » Rotating Frames

Appeared in Year: 2013

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A satellite revolves in a circular orbit around the Earth at a certain height above it. Calculate the time period of revolution of the satellite, if the radius of the Earth is significantly higher than the height at which the satellite revolves. (Section A)

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