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Q.

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_II

A)  Body in stable equilibrium                P) Rotational kinetic energy

 B)  Body in unstable equilibrium           Q) Minimum potential   

                                                                 energy

C)   Body in neutral equilibrium         R)Maximum potential energy

D) Body in pure rotational motion     S) Constant potential energy

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a

A-R; B-S; C-P D-Q

b

A-P; B-Q; C-R D-S

c

A-S; B-Q; C-P D-R

d

A-Q; B-R; C-S D-P

answer is D.

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Detailed Solution

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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