Question

Which of the following sets of concurrent forces may be in equilibrium?

• A. $F_1=3\text{N},F_2=5\text{N},F_3=1\text{N}$
• B. $F_1=3\text{N},F_2=5\text{N},F_3=9\text{N}$
• C. $F_1=3\text{N},F_2=5\text{N},F_3=6\text{N}$
• D. $F_1=3\text{N},F_2=5\text{N},F_3=15\text{N}$

Answer 1

The correct option is C

$F_1=3\text{N},F_2=5\text{N},F_3=6\text{N}$

Step 1:Formula Used: For three concurrent forces to be in a state of equilibrium, the condition is as given below:
$F_1+F_2⩾F_3$

Step 2:According to the triangle law of forces:

three forces are said to be in a state of equilibrium only if the sum of any two forces given is either greater than or equal to the third force. Thus, mathematically the triangle law of forces can be written in the following way:
$F_1+F_2⩾F_3$
Now, we can solve the given numerical problem by substituting the forces in the given equation:
Step 3:In case (A) $F_1=3N,F_2=5N,F_3=1N$now when we substitute these values in the above equation, we get:
$3N+5N>1N$
But, we see that $F_1+F_3\ne F_2$ as $3N+1N<5N$. Thus, we can conclude that in condition (A) the forces are not in a state of equilibrium. Thus, option (A) is an incorrect answer.
In case (B) $F_1=3N,F_2=5N,F_{{}_3}=9N$ now when we substitute these values in the given mathematical expression, we get:
$3N+5N<9N$. Thus, we find that it does not satisfy the condition $F_1+F_2⩾F_3$.
Thus, we can conclude that in condition (B) is an incorrect answer as the forces are not in equilibrium.
Now for condition (C) we can clearly see that $3N+5N>6N$. Thus, we can say that in this case the three forces are in equilibrium in accordance with the triangle law of forces.
Thus we find that (C) is the correct answer to this question.