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EEJ MAIN Physics QUESTION #7017
Question 1
A mass of $10\text{ kg}$ is suspended vertically by a rope. A horizontal force is applied to the rope at a specific point, causing the rope at the ceiling to deviate by an angle of $45^\circ$. If the system is in equilibrium, what is the magnitude of the horizontal force? (Assume $g = 10\text{ ms}^{-2}$)
  • $200\text{ N}$
  • $140\text{ N}$
  • $70\text{ N}$
  • $100\text{ N}$✔️
Correct Answer Explanation
At equilibrium, the horizontal component of the tension $T \sin(45^\circ)$ equals the applied force $F$, and the vertical component $T \cos(45^\circ)$ equals the weight $mg$. Dividing the two equations gives $F = mg \tan(45^\circ)$. Since $\tan(45^\circ) = 1$ and $mg = 10 \times 10 = 100$, the force $F = 100\text{ N}$.