Question on: JAMB Physics - 2020

Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?

I. P\(_1\) sin \(\theta_1\) = p\(_1\) cos \(\theta_2\)

II. P\(_3\) = P\(_1\) cos \(\theta_4\) + P\(_2 cos_2\)

III. P\(_1 \sin \theta_1 = P_2 \sin \theta_2\)

I only

II only

III only

I, II and III only

Ask EduPadi AI for a detailed answer

Correct Option: C

Here's the breakdown to determine the correct equation(s): * **Understanding Equilibrium:** For a system to be in equilibrium, the net force in any direction must be zero. This means the sum of forces in the x-direction equals zero, and the sum of forces in the y-direction equals zero. * **Analyzing the Equations:** * **I. P₁ sin θ₁ = P₁ cos θ₂:** This equation is incorrect because it equates a component of P₁ (y-component) to another component of P₁ (x-component) which is not a valid equilibrium condition. * **II. P₃ = P₁ cos θ₄ + P₂ cos θ₂:** This equation is incorrect. It attempts to relate P₃ to the x-components of P₁ and P₂, which is not generally valid. * **III. P₁ sin θ₁ = P₂ sin θ₂:** This equation is correct. For equilibrium, the upward forces must equal the downward forces in the y-direction. Assuming that P1 and P2 have x-components and y-components, this is a statement of equilibrium in the y-direction. * **Conclusion:** Therefore, only equation III is correct.