Force Systems and Resultants Questions and Answers

Answer: B

Let \(\theta\) be the angle between the vectors and \(c = \cos\theta\). Then \(R^2 = A^2 + B^2 + 2ABc\). Doubling B gives \(4R^2 = A^2 + 4B^2 + 4ABc\), and reversing B gives \(4R^2 = A^2 + B^2 - 2ABc\). Subtracting the last two: \(3B^2 + 6ABc = 0\), so \(2ABc = -B^2\).

So \(A : B : R = 1 : \sqrt{3/2} : 1 = \sqrt{2} : \sqrt{3} : \sqrt{2}\). The ratios 2:3:2 and 2:1:3 are not consistent with R equal to A.

Answer: A

Coplanar forces are forces whose lines of action all lie in one plane, which is the first option. Forces acting at a single point are concurrent forces, a single force that keeps the body in equilibrium together with other forces is the equilibrant, and a single force that produces the same effect as two or more forces is the resultant. So the other three options define different terms. In coplanar force systems all the forces can be shown on a flat drawing, and this is the common case in statics problems.

Answer: A

All three statements are true. Physical quantities with only magnitude, such as mass and time, are scalars. Quantities with both magnitude and direction, such as velocity and force, are vectors. Two equal and opposite parallel forces acting at different points of a body constitute a couple, which tends to turn the body without moving it as a whole. Since all three are true, the options that mark any of them false are wrong. The turning effect of a couple is its moment, which is the force times the perpendicular distance between the two lines of action.