Question

An object O is in equilibrium under four concurrent forces in direction as shown in figure. The value
of Fris
130° AN
60°
-
30%
→ 8N
KF,​

Answer 1

Answer:

$(2) \frac{20}{\sqrt{3}} N$

Explanation:

1) Since, Object O is in Equilibrium .

Hence,

$\sum F_x = 0 \\ \\=> 4 cos(60^{\circ})+8 - F_2cos(30^{\circ})=0 \\ \\=>4*\frac{1}{2}+ 8-F_2cos(30^{\circ})=0\\ \\=>2+8=F_2\frac{\sqrt{3}}{2}\\ \\=>F_2 = \frac{20}{\sqrt{3}} N$

Hence, Correct Answer is option (2)

However,

If we need to find , value of  F_1.

$\sum F_y=0\\ \\=>F_1+4cos(30^{\circ})-F_2sin(30^{\circ})=0\\ \\=>F_1 +2\sqrt{3}=\frac{10}{\sqrt{3}}\\ \\=>F_1 = \frac{4}{\sqrt{3}} N$

Answer 2

Answer:

F₂ = 20/√3

Explanation:

As object O is in equilibrium

Let say Find x component of All forces as

8N

4Cos60 = 4/2 = 2N

-F₂Cos30 = -F₂√3 /2

8 + 2 - F₂√3 /2  = 0

=> F₂√3 /2  = 10

=> F₂ = 20/√3

Additional Info :

-F₂Sin30 = -10/√3

4Sin60 = 2√3

F₁ + 2√3  = 10/√3

=> F₁ + 6/√3   = 10/√3

=> F₁ = 4/√3