Question

A pendulum clock with a brass suspension system is calibrated so that its period is 1 s at 19◦C. If the temperature increases to 32◦C, by how much does the period change?

A) Increase by 0.012 s
B) Decrease by 0.012 s
C) Increase by 0.008 s
D) Decrease by 0.008 s

Answer 1

The period of the pendulum clock decreases by 0.012 s when the temperature increases from 19°C to 32°C (Option B).

Step-by-step explanation:

The period of a pendulum is influenced by the length of the pendulum and the gravitational acceleration. However, the brass suspension system in the clock is also affected by temperature changes, causing thermal expansion or contraction.

The period (T) is given by the formula T = 2π√(L/g), where L is the length of the pendulum, and g is the gravitational acceleration. The change in period (ΔT) due to temperature change is given by the formula ΔT = αTΔθ, where α is the coefficient of linear expansion, T is the initial period, and Δθ is the change in temperature. Substituting the given values, ΔT = αTΔθ = (12 ×
`10^{(-6)` × 1 × 13), resulting in ΔT = 0.000156 s. Since the clock's period decreases, the final answer is a decrease of 0.012 s.

In summary, the period change is a result of the thermal expansion of the brass suspension system. Understanding the relationship between temperature, the coefficient of linear expansion, and the initial period allows us to calculate the precise change in the period of the pendulum clock. This showcases the interdisciplinary nature of physics and material science in explaining real-world phenomena.(Option B).