9702/May Jun/13/2015/Q16

The diagrams represent systems of coplanar forces acting at a point. The lengths of the force
vectors represent the magnitudes of the forces.

Which system of forces is in equilibrium?

Solution:

Answer: A.

For the forces to be in equilibrium, the resultant horizontal and vertical components of the force vectors should be zero.

The lengths of the vectors represent the magnitudes. Note that the diagonal vectors in the diagrams will have vertical and horizontal components less than the magnitude of the diagonal vector itself {this is obvious since the diagonal vector and its components form a right-angled triangle with the diagonal vector as the hypotenuse. The hypotenuse has the longest length in a right-angled triangle}.

Therefore, in these diagrams, the horizontal and vertical components of the diagonal vectors should be equal in length (and opposite in direction) as the horizontal and vertical vectors already given.

Diagram A:
The horizontal and vertical components of the diagonal vector are equal in magnitude and opposite in direction to the respective vectors already given. So, in diagram A, the system of forces is in equilibrium.

Diagram B:
The sum of the upward vertical components of the 2 diagonal vectors is greater than the downward vertical vector already present. So, the system of forces is not in equilibrium.

Diagram C:
The sum of the horizontal components (toward the left) of the 2 diagonal vectors is smaller than the horizontal vector (toward the right) already present. So, the system of forces is not in equilibrium.

Diagram D:
The system is not balanced vertically since the downward vertical component of one of the diagonal vectors is greater than the upward vertical component of the other diagonal vector.

Reference: PYQ - May/Jun 2015 Paper 13 Q16