Question

An aluminum pendulum that is 2m long at 30 degrees Celcius has a period of 2.83845 seconds. If the period is increased by 0.04% what is the temperature of the aluminum pendulum?

Answer 1

We know the time period of pendulum is,

, where L=length of the pendulum, g=gravitational acceleration.

Initial time period is, T_i=2.83845 sec, initial length, Lo=2 m, temperature,t=30 degree C.

final time period, T_f = T_i +0.04% =2.83885 sec, So final length is, .

The effective length of pendulum  has changed, means there is a change in temperature.

using the formula, . where is thermal linear expansion coefficient and is temperature change.

For aluminum .

So,