The condition of equilibrium is satisfied when resultant of all forces acting on body vanishes and also no net torque acts on the body. However body can be different types of equilibrium as stable, unstable, neutral or may be having pure rotation when no resultant force acts on the body. Different conditions of equilibrium or rotational motion can be known by different types of energy it possesses. Column I mentions the state of body and column II mentions the type of energy it possesses. Match the correct options in two columns $$COLUMN_I$$ $$COLUMN_IIA)$$ Body in stable equilibrium $$P)$$ Rotational kinetic energy $$B)$$ Body in unstable equilibrium $$Q)$$ Minimum potential $$energyC)$$ Body in neutral equilibrium $$R)Maximum$$ potential $$energyD)$$ Body in pure rotational motion $$S)$$ Constant potential energy

Question

The  condition of equilibrium is satisfied when resultant of all forces acting on  body vanishes and also no net torque acts on the body. However body can be  different types of equilibrium as stable, unstable, neutral or may be having  pure rotation when no resultant force acts on the body. Different conditions  of equilibrium or rotational motion can be known by different types of energy  it possesses. Column I mentions the state of body and column II mentions the  type of energy it possesses. Match the correct options in two columns  $$COLUMN_I$$                                                              $$COLUMN_IIA)$$  Body in stable equilibrium                $$P)$$ Rotational kinetic energy $$B)$$  Body  in unstable equilibrium           $$Q)$$ Minimum  potential                                                                    $$energyC)$$    Body in neutral equilibrium         $$R)Maximum$$ potential $$energyD)$$  Body in pure rotational motion     $$S)$$ Constant  potential energy

Infinity Learn · Accepted Answer

When  body is in state of minimum potential energy the force on body $$F=$$−$$dUdx=0$$     . If body is distributed from mean position the body will  try to come mean position the body will try to come back to equilibrium  position as restoring force will be developed in it with the condition that  if $$dx=+ve$$     , $$F=$$−ve      and if $$dx=$$−ve     , $$F=+ve$$     . So the force developed will try to maintain the position  of body. For stable equilibrium $$d2Udx2=+ve$$       Alternative:For  given curve U      is minimum, at C     Slope  at C     , $$dUdx=0$$     ; at A     , $$dUdx=$$−ve     , hence ∴      $$FA=$$−$$dUdx=+ve$$     At  B     , $$dUdx=+ve$$     , hence FB      is −ve     .This  shows force is directed towards mean position always

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