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Which of the given statements are correct for a conservative force field (p) The total mechanical energy is conserved. (q) The work done around a closed path is zero. (r) Gain in kinetic energy = Loss in potential energy.

Which of the given statements are correct for a conservative force field (p) The total mechanical energy is conserved. (q) The work done around a closed path is zero. (r) Gain in kinetic energy = Loss in potential energy. Correct Answer (p), (q) & (r)

CONCEPT:

  • Conservative force: A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
  • Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are the examples of a conservative force.
  • Non-conservative forces: A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
  • Example:  Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:​

[ alt="closedloop" src="//storage.googleapis.com/tb-img/production/20/09/closedloop.gif" style="width: 230px; height: 170px;">

  • Suppose a particle starts at A and a force Fext is acting on it. The particle is moved around the loop using the same force, Fext
  • Suppose the particle eventually ends up at A itself then the entire displacement of the particle is zero which means the total work done is zero.
  • A total work one zero means there is no expenditure of energy which means the total energy is conserved. Hence statement p is correct
  • The total displacement of a particle in a closed loop is zero, which means total work done is zero. Hence statement q is correct.
  • The total mechanical energy of a system is given by 

⇒ Total energy = Potential Energy + Kinetic energy

  • From the statement p, it is clear that if the total work done is zero which means the energy is conserved.
  • Which means Gain in kinetic energy = Loss in Potential Energy. Hence option r is correct.

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