Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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

  1. AF₂=-(2+ 3 ) F₁: F₃= -4 6 - 2 F₁
  2. BF₂=-(2- 3 ) F₁: F₃= -4 6 + 2 F₁
  3. CF2 = [-F1 (2 + √3)]; F3= [√6-√2]F1
  4. 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

Practice Laws of Motion on Quantrex Academy →

More from Laws of Motion

A block of metal, of 25g mass moves down without acceleration when the plane is inclined at an angle of 30^ . When the inclination is increased by 30^ , find the downward accelerat 2026A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 6 m/s ^2 . What would be his weight in kg? ( g = 10 m/s ^2 ) 2026A mass M is hung with a light inextensible string as shown in figure. Find the tension of the horizontal string. 2026A horizontal force of 5 N is applied on a stationary body of mass 5 kg, which is initially at rest on a frictionless table. The change in kinetic energy of the body in 10 s is 2026The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of 2 ~ms ⁻² is (Acceleration due to gravity =10 ~m ~s ⁻² ) 2025If a stone of mass 0.5 kg tied to one end of a wire is whirled in a circular path of radius 2 m with a speed 40 rev / min in a horizontal plane, then the tension in the wire is nea 2025If the breaking strength of a rope is 4 3 times the weight of a person, then the maximum acceleration with which the person can safely climb up the rope is (g - accelereation due t 2025A block of mass 2 kg is placed on a rough horizontal surface. If a horizontal force of 20 N acting on the block produces an acceleration of 7 ~m ~s ⁻² in it, then the coefficient o 2025 Full Laws of Motion list All AP EAMCET PYQs