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JAMB Physics 2020 Paper

Question : 23

Total: 38

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 ${}_1$ cos $\theta_1$ = p ${}_1$ cos $\theta_2$

II. P ${}_3$ = P ${}_1$ cos $\theta_4$ + P ${}_2 \cos_2$

III. P ${}_1 \sin \theta_1 = P_2 \sin \theta_2$

Solution:

Concept:

For forces acting at a point to be in equilibrium, their resolved components must balance in each direction.

Explanation:

Resolve the three forces into horizontal and vertical components.

For vertical equilibrium:

P_1 \sin\theta_1 - P_2 \sin\theta_2 = 0

Therefore:

P_1 \sin\theta_1 = P_2 \sin\theta_2

This matches statement III.

For horizontal equilibrium:

P_1 \cos\theta_1 + P_2 \cos\theta_2 - P_3 \cos\theta_0 = 0

So:

P_3 \cos\theta_0 = P_1 \cos\theta_1 + P_2 \cos\theta_2

This is not the same as statement I or II as written.

Hence, only the vertical component equation given as III is correct.

Answer:

C. III only

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