Question

The answer is c but shouldnot it be d

Answer 1

c. 10.0 N

Step-by-step explanation:

To solve this problem, we can apply the principles of equilibrium for forces and moments. Since the rod is in equilibrium, the sum of moments about any point is zero. By taking moments about point X (where the rod is attached), we can solve for the force 'F'.

Let 'L' be the length of the rod. Now taking the sum of moments about point X:

`\sum M_X: -F_g\left((L)/(2)\right)+FL\sin(\theta)=0\\\\\\\\\Longrightarrow -(10\text{ N})\left((L)/(2)\right)+FL\sin(30 \textdegree)=0\\\\\\\\\Longrightarrow -(5\text{ N})L+FL\sin(30 \textdegree)=0\\\\\\\\\Longrightarrow FL\sin(30 \textdegree)=(5\text{ N})L \Big] \cdot (1)/(L)\\\\\\\\\Longrightarrow F\sin(30 \textdegree)=5\text{ N}\\\\\\\\\Longrightarrow F=\frac{5\text{ N}}{\sin(30 \textdegree)}\\\\\\\\\therefore F = \boxed{10 \text{ N}}`

Thus, option (c) is correct.