Question

Any number of coplanar forces acting on a rigid body can be reduced to
(a) a single force
(b) a single couple
(c) either to a single force or a single couple
(d) a single force together with a couple

Answer 1

In order to calculate the number of coplanar forces acting on a rigid body can be reduced to, we need to use the concept of scalar and vectors. This will help us to define this situation.

Complete step-by-step answer:
Any number of forces can be resolved to concurrent forces and respective couples. Further, the concurrent forces can be combined to get a single resultant force, and also the couples can be added algebraically to get a single couple. With this it can be deduced to the required solution i.e. a single force together with a couple.

Thus, the correct answer to this question is option (d).

Additional Information: Scalar quantity is defined as the physical quantity with magnitude and no direction. Some physical quantities can be described just by their numerical value (with their respective units) without directions (they don’t have any direction). The addition of these physical quantities follows the simple rules of the algebra. Here, only their magnitudes are added. For example, mass, speed, distance, etc. Whereas, A vector quantity is defined as the physical quantity that has both direction as well as magnitude. A vector with the value of magnitude equal to one and direction is called an unit vector represented by a lowercase alphabet with a “hat” circumflex ($\hat u$). For example, Acceleration, Displacement, Momentum, etc.

Note: While solving this question, we should have the basic knowledge of scalar and vector quantities. Concept of these will be used to solve this question. Some of the basic concepts are mentioned above.