A grandfather clock is controlled by a swinging brass pendulum that is 1.3m long at a temperature of?

Question

A grandfather clock is controlled by a swinging brass pendulum that is 1.3m long at a temperature of 20 degree's celcius.

(A) what is the length of the pendulum rod when the temperature drops to 0 degrees celcius?

(B) if a pendulum's period is given by t=2pi(square root of L/g),
where l is its length, does the change in length of the rod cause the clock to run fast or slow?.

Answer 1

A )When temperature drops from T2 to T1 the length L will decrease by dL .

dL=uL(T1-T2) ( you will get a negative value)
where u - coefficient of linear expansion

The new length L2 will be
L2= L + dL

B) As you have pointed out T=2pi sqrt(L/g) the decrease in L will cause a decrease in period of oscillation and the clock will run faster.

Answer 2

i don't understand one in all those math yet can assume that the clock might relaxing quicker as a results of fact the rod is shorter? Hell I dunno, merely get an iPhone and u won't could hardship approximately whether your clock is shifting rapid or sluggish!