What is the magnitude of the resultant of two like parallel forces 10 N and 30 N separated by a distance of 10 cm?

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  1. 20\(\sqrt{2}\) N
  2. 10\(\sqrt{10}\) N
  3. 20 N
  4. 40 N

Answer (Detailed Solution Below)

Option 4 : 40 N
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Explanation:

The resultant magnitude of two like (same direction) parallel forces is the algebraic sum of the forces. This is due to the principle of superposition, which states that when two or more forces are acting on a body, each force will have the same effect as if it were acting alone.

The two forces here are 10 N and 30 N and since they are in the same direction, you can add them directly:

Resultant = 10 N + 30 N = 40 N

The resultant vector's direction will be the same as the direction of individual forces. The separation distance between the forces does not affect the magnitude of the resultant in the case of like parallel forces, it only influences the location of the line of action of the resultant force. Hence, the magnitude of the resultant force is 40 N.

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