Question

Vector sum of two forces of 10N and 5N can be : (1) 4N (2) 18N (3) 12N (4) 2N​

Answer 1

Answer:

answer of this question is (3) 12N

Answer 2

Therefore Vector sum of two forces given 10 N and 5 N can be 12 N. ( Option 3 )

Given:

Two forces are 10 N and 5 N

To Find:

The vector sum of the given forces.

Solution:

This numerical can be solved in the following way.

Let forces are named as F₁ = 10 N and F₂ = 5 N

Here, three cases are possible.

Case 1:

If 2 forces are in the same direction then both the forces are positive in nature.

F₁ = 10 N and F₂ = 5 N

⇒ F₁ + F₂ =  10 + 5 = 15 N

Case 2:

If 2 forces are in different directions then one force is positive and another is negative.

F₁ = 10 N and F₂ = -5 N

⇒ F₁ + F₂ = 10 + ( -5 ) = 5 N

Case 3:

If both of the forces are at right angles then,

F₁ = 10 N and F₂ = 5 N

⇒ Resultant = √ F₁² + F₂² = √ 10² + 5²  = √ 125 = 11.18 ≅ 12.

Or we can simply see the vector addition simply remains between Minimum Vector addition ( When both the forces are in opposite directions F = 15 N ) and Maximum Vector addition ( When both the forces are in the same direction F = 5 N )

So the force should be present between Maximum Vector addition and Minimum Vector addition. ( 5 < F < 15 )

Therefore Vector sum of two forces given 10 N and 5 N can be 12 N.

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