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

Which of the following sets of concurrent forces may be in equilibrium?
  1. \(F_1=3 \mathrm{~N}, F_2=5 \mathrm{~N}, F_3=10 \mathrm{~N}\)
  2. \(F_1=3 \mathrm{~N}, F_2=5 \mathrm{~N}, F_3=9 \mathrm{~N}\)
  3. \(F_1=3 \mathrm{~N}, F_2=5 \mathrm{~N}, F_3=6 \mathrm{~N}\)
  4. \(F_1=3 \mathrm{~N}, F_2=5 \mathrm{~N}, F_3=15 \mathrm{~N}\)

Solution

According to triangle law of forces, resultant of two forces must be greater than or equal to the third force. In option (a), \(F_1(3 \mathrm{~N})+F_3(1 \mathrm{~N}) < F_2(5 \mathrm{~N})\) Hence, these sets of concurrent forces may not in equilibrium. In option (b), \(F_1(3 \mathrm{~N})+F_2(5 \mathrm{~N}) < F_3(9 \mathrm{~N})\) Hence, these sets of concurrent forces also may not in equilibrium. In option (c), \(F_1(3 \mathrm{~N})+F_2(5 \mathrm{~N}) > F_3(6 \mathrm{~N})\) Hence, these sets of concurrent forces may be in equilibrium. In option (d), \(F_1(3 \mathrm{~N})+F_2(5 \mathrm{~N}) < F_3(15 \mathrm{~N})\) Hence, these sets of concurrent forces may not in equilibrium.

Asked in: AP EAMCET 2020 (17 Sep Shift 2)

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