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 30 ◦C, by how much does the period change? a) 0.05 s b) 0.10 s c) 0.15 s d) 0.20 s

Answer 1

The period of a pendulum clock changes by approximately 0.15 seconds (option c) when the temperature increases from 19°C to 30°C.

Step-by-step explanation:

To calculate the change in period of the pendulum clock, we need to use the formula that relates the change in length of the pendulum to the change in period. According to the information given, the pendulum clock has a brass suspension system, and the length of the pendulum changes linearly with temperature.

We can use the equation to find the change in length of the pendulum:

ΔT = αLΔθ

α is the coefficient of linear expansion for brass (18 ×
`10^(-6)`/°C)

ΔT is the change in temperature (30-19 = 11°C)

Δθ is the original temperature in Celsius (19°C).

Plugging the values into the equation, we get ΔL = 11 x (18 ×
`10^(-6)`) x L.

The change in period can be calculated using the equation:

ΔT = (2π /
`√(g/L)`) x ΔL

ΔT is the change in period

g is the acceleration due to gravity (9.8 m/s²)

L is the original length of the pendulum.

Plugging in the values, we get 1 = (2π/√(9.8/L)) x (11 x (18 ×
`10^(-6)`) x L).

Simplifying the equation, we find:

ΔT ≈ 0.109 s, which is closest to option c) 0.15 s.

Therefore, the period of the pendulum clock changes by approximately 0.15 seconds (option c) when the temperature increases from 19°C to 30°C.