AP EAMCET20228 Jul 2022Evening ShiftPhysicsLaws of MotionActual
Three forces of magnitude F₁, F₂ and F₃ act on a body located at the origin as shown in the figure. The condition that gives zero net force is
Options
- AF₂=-(2+ 3 ) F₁: F₃= -4 6 - 2 F₁
- BF₂=-(2- 3 ) F₁: F₃= -4 6 + 2 F₁
- CF2 = [-F1 (2 + √3)]; F3= [√6-√2]F1
- DF₂=-(2+ 2 ) F₁: F₃= -2 6 - 2 F₁
Correct answer
C. F2 = [-F1 (2 + √3)]; F3= [√6-√2]F1
Step-by-step solution
Forces given are as shown Resolving components we have, For equilibrium ; F_y=0F₂ 60^ +F₁ 30^ =F₃ 45^ F₂ 3 2 +F₁ 1 2 =F₃ 1 2 3 F₂+F₁= 2 F₃ ...(i) and F_x=0F₂ 60^ =F₃ 45^ +F₁ 30^ F₂ 1 2 =F₃ 1 2 +F₁ 3 2 F₂= 2 F₃+ 3 F₁ ...(ii) Subtracting eq. (ii) from eq. (i) we get, 3 F₂+F₁-F₂=- 3 F₁ array rrr & ( 3 -1) F₂=-F₁(1+ 3 ) & F₂=F₁ ( 1+ 3 1- 3 ) array array ll & F₂=- F₁( 3 +1)^2 ( 3 -1)( 3 +1) & F₂= -F₁(3+1+2 3 ) 3-1 array or F₂=-F₁(2+ 3 ) Now, putting the value of F₂ in eq. (i), we get aligned 3 [-F₁(2+ 3 ) ]+F₁ & = 2 F₃