Question

A pendulum of length L₁ has a period T₁ =0.960 s. The length of the pendulum is adjusted to a new value L₂ such that T₂ =1.40 s. What is the ratio L₂ /L₁ ?

Answer 1

The ratio of the new adjusted length of the pendulum L₂ to the original length L₁, with periods T₂ and T₁ respectively, can be found by squaring the ratio of the periods (T₂/T₁)², resulting in a length ratio of approximately 2.144.

Step-by-step explanation:

The student is asking about the relationship between the length of a pendulum and its period. Using the formula T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity, we see that the period of a pendulum is directly proportional to the square root of its length. Therefore, if the period T₁ = 0.960 s for length L₁, and the period T₂ = 1.40 s for the adjusted length L₂, we can set up a ratio to find the relationship between L₂ and L₁.

First, we take the ratio of the two periods squared:

((T₂/T₁)² = (L₂/L₁))

((1.40/0.96)² = (L₂/L₁))

Calculate the left side of the equation:

(1.46² = (L₂/L₁))

Finally, we get the ratio L₂/L₁, which is approximately 2.144. So the length L₂ is approximately 2.144 times that of L₁.