The difference in temperature between summer and winter causes the length of a pendulum in a clock to change by one part in 27000. If the period of the pendulum is 1 s, what time-difference error will this make in one hour?

Answer 1

t=2pisqrt( L/g)
t'=2PI/2* l'/sqrt(l/g)

t'= PI l'/(t/2PI)

t'=2pi^2 l'/t
so l'=1/27000, t=1
t'=0.000731081807 sec, per second.

In an hour, t'=3600*t'
= 2.63 sec check that.