4. suppose the pendulum of a grandfather clock expands because of heat. will it overcount or undercount time?

under count

Explanation:

Time period of simple pendulum clock is given by

where L=length of pendulum

g=acceleration due to gravity

With increase in temperature there is increase in length as material expands with increasing temperature

and time period is inversely proportional to the square root of length therefore time period decreases and it under counts time