WAEC 2011 Physics · Question 21

Two simple pendulum A and B of equal lengths and of masses 5g and 20g respectively are located in the same…

Question

Two simple pendulum A and B of equal lengths and of masses 5g and 20g respectively are located in the same environment. The periods TA and TB of their respective oscillations are related by the equations

A.TA = 4TB
B.TA = $\frac{1}{4} T_B$
C.TA = TB
D.TA = 5TB

Answer: C. TA = TB

Explanation written with AI and checked against the answer key

Analyze the question: Two simple pendulums have the same length but different masses (5 g and 20 g). They are in the same place, so g is the same. We need the relationship between their periods. Concept: The period of a simple pendulum is T = 2π√(L/g) The formula contains only the length L and the acceleration due to gravity g. The mass of the bob does not appear in it. Solution: For pendulum A: TA = 2π√(L/g) For pendulum B: TB = 2π√(L/g) Both have the same L (equal lengths) and the same g (same environment), so: TA = TB The 5 g and 20 g masses are a distraction. Mass cancels out because gravity's pull on the bob is proportional to its mass, but so is its inertia. A heavier bob feels a bigger restoring force but also resists acceleration more, so the two effects cancel. Answer: Option C, TA = TB. Tip: In pendulum questions, the period depends only on length and g. If the question gives different masses, it is almost always a trap. Likewise, a small change in amplitude does not matter as long as the angle stays small.

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