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If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is:

A. 1
B. 2
C. 3
D. 4

1 Answer

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Final answer:

In three-dimensional space, a minimum of 4 forces is necessary for the resultant of forces acting at a point to be zero, demonstrating equilibrium.

Step-by-step explanation:

If the resultant of n forces acting at a point is zero, they must be in equilibrium. For forces in a plane (two-dimensional), the minimum number of forces required to achieve this is 3. These three forces, when carefully chosen, can act in such a way that they cancel out each other. However, this is the minimum for two-dimensional interactions. When dealing with forces in three dimensions, a minimum of 4 forces is necessary. Here's why: Imagine trying to balance a force coming from the north with a force from the south; you've balanced in the north-south axis. Adding two more forces from the east and west will balance forces in the east-west axis. Now, if there is a force acting upward, we need a fourth force acting downward to balance the force in the vertical axis. Thus, a total of at least four forces is needed to achieve equilibrium and make the resultant force zero in three-dimensional space.

This is confirmed by available examples, such as three forces acting on an object where the necessary condition is their net effect creating a zero resultant for an object to move in a specific direction, or the use of a free-body diagram to calculate the interaction of forces.

User Venkata Gogu
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