In a certain clock, a pendulum of length L₁ has a period T₁ = 0.95 s. The length of the pendulum is adjusted to a new value L₂ such that T₂ = 1.0 s. What is the ratio L₂/L₁? A)0.90 B)0.95 C)1.0 D)1.1 E)1.3

Question

Quizplus · Accepted Answer

The period T of a pendulum is given by the formula T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Therefore, we have T1=2π√(L1/g) and T2=2π√(L2/g), where T1=0.95 s, T2=1.0 s, and L1=L₁. Dividing these two equations gives us T2/T1=√(L2/L1), which can be rearranged as L2/L1=(T2/T1)^2. Substituting the given values, we have L2/L1=(1.0/0.95)^2=1.102. Therefore, L₂/L₁= L2/L1=1.102, which is closest to 1.1. Thus, the answer is D) 1.1.

In a Certain Clock, a Pendulum of Length L1 Has

In a Certain Clock, a Pendulum of Length L₁ Has