Question

A single force and coplanar couple together acting on a rigid body are equivalent to
A. A couple
B. A single force equal to the given force and in any direction
C. A single force and parallel to given force
D. None of these

Answer 1

Hint: A system of coplanar forces acting on a body can be reduced to either a single force or a single couple. Any force is equivalent to an equal and parallel force acting at an arbitrary point together with a couple. Moment of this couple is equal to the moment of the given force at that point. We can resolve a single force and coplanar couple as a parallel force at some distance.

Complete answer:
By the definition of the couple we know, two equal and unlike parallel forces with different lines of actions are said to form a couple. Force applied to a key of a lock either to lock it or unlock it is an example of a couple.
A single force and a coplanar couple together acting on a rigid body are equivalent to a single force and also parallel to the given force.
So, the correct answer is option C i.e. a single force and parallel to given force.

So, the correct answer is “Option C”.

Note:
A single force and a coplanar couple together acting on a rigid body cannot produce the state of equilibrium. To produce a state of equilibrium, another couple of equal magnitude and opposite direction in the same plane or in the parallel plane has to exist. Moment of a couple about any point in a plane is constant, both in direction and magnitude. Couple produces a pure rotational motion in the body.