Which of the following sets of concurrent for | vedclass

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(D) For three concurrent forces to be in equilibrium,the magnitude of any one force must be less than or equal to the sum of the other two and greater

Vedclass · Accepted Answer

$F_1 = 3 \, N, F_2 = 5 \, N, F_3 = 6 \, N$

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(D) For three concurrent forces to be in equilibrium,the magnitude of any one force must be less than or equal to the sum of the other two and greater than or equal to the difference of the other two.Mathematically,for forces $F_1, F_2, F_3$,the condition is $|F_1 - F_2| \leq F_3 \leq F_1 + F_2$.Given $F_1 = 3 \, N$ and $F_2 = 5 \, N$,the range for the third force $F_3$ to maintain equilibrium is $|5 - 3| \leq F_3 \leq 5 + 3$,which simplifies to $2 \, N \leq F_3 \leq 8 \, N$.Checking the options:$(a)$ $9 \, N$ is outside the range $[2, 8]$.$(b)$ $1 \, N$ is outside the range $[2, 8]$.$(c)$ $15 \, N$ is outside the range $[2, 8]$.$(d)$ $6 \, N$ is within the range $[2, 8]$.Thus,the set of forces $3 \, N, 5 \, N, 6 \, N$ can be in equilibrium.

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

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