A grandfather clock has a simple brass pendulum of length

                                                 Solution to 88GP

Step 1 of 3

We need to find the actual time the clock shows at 10 AM in the morning if the brass pendulum of length  and time period  at a temperature of  changes in temperature to  at 10 P.M.

In order to solve this problem, we need to understand the connection between the length of the pendulum and the temperature.

We know that the time period of the pendulum is given as,

Thus,

Now, as the temperature changes the length of the pendulum also changes,

Here,

 is the final length,

 is the original length,

 is the coefficient of thermal expansion,

 is the change in temperature,