Question

Your grandfather clock's pendulum has a length of 0.9930 m. if the clock loses 60 seconds per day, should you increase or decrease the length of the pendulum?

Answer 1

Pendulum should be decreased to 0.9914m

Step-by-step explanation:

The clock losses 60seconds per day.

In a day,there are 24×60×60=86400seconds/day

The period T= 2pisqrt(L/g)

T= 2×3.142sqrt(0.9930/9.8)

T= 2.00005277seconds

Error ratio=60/86400= 6.94×10^-4

Terror= 2.00005277×6.94×10^-4=1.389×10^-3seconds

Tcorrect=Toriginal -T error

Tcorrect= 2.00005277- 1.389×10^-3=1.998seconds

T=2pisqrt(L/g)

Solving for L

T/2pi = sqrt(L/g)

T^2/(2pi)^2=(L/g)

L =( g× T^2) / (2pi)^2

L= (9.8×(1.9987)^2/(2×3.142)^2

L = 39.188/39.4887

L = 0.9914m

Pendulum should be decreased to 0.9914m.

Answer 2

We have to speed up the watch so we need to decrease time period of pendulum. So we hv to reduce the length.