Out of the following pairs of forces, the resultant of which...

Out of the following pairs of forces, the resultant of which can not be $18 \mathrm{~N}$
(A) $11 \mathrm{~N}, 7 \mathrm{~N}$
(B) $11 \mathrm{~N}, 8 \mathrm{~N}$
(C) $11 \mathrm{~N}, 29 \mathrm{~N}$
(D) $11 \mathrm{~N}, 5 \mathrm{~N}$

Key Concepts

Resultant Force

The resultant force is the vector sum of two or more individual forces acting on an object. It represents the overall effect of these forces and determines the object's acceleration according to Newton's second law. Understanding resultant forces is crucial in mechanics as it helps in analyzing the net effects of multiple forces acting in different directions.

Vector Addition

Vector addition is a fundamental process in physics where forces, represented as vectors, are combined by adding their corresponding components. This operation takes into account both the magnitude and direction of each force, resulting in a new vector that accurately reflects the combined influence of the original vectors.

Triangle Inequality

The triangle inequality is a principle that provides bounds on the possible magnitude of the resultant vector when two vectors are added. It states that the magnitude of the resultant must be less than or equal to the sum of the individual magnitudes and greater than or equal to the absolute difference of the individual magnitudes. This concept is essential for understanding the range of possible values when combining forces.

Angle Between Forces

The angle between forces is a critical factor in vector addition as it affects the magnitude of the resultant force. When two forces act at an angle to each other, the resultant is determined not only by the magnitudes of the forces but also by the cosine of the angle between them. This concept is key in calculations involving non-parallel forces.

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