Question
If the sum of all the forces acting on a body is zero, is it necessarily in equilibrium? If the sum of all the forces on a particle is zero, is it necessarily in equilibrium?

Answer

No, if the sum of all the forces acting on a body is zero, the body is not necessarily in equilibrium. To be in equilibrium, the sum of torque acting on the body must be zero too. In the above case, although the sum of the forces acting on the body is zero $\Big(\vec{\text{F}}_1+\Big(-\vec{\text{F}}_1\Big)=0\Big).$ Still, the body will rotate along $\overrightarrow{\text{OP}}.$ So, it won't remain in equilibrium.

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