Question

A pendulum clock uses a simple pendulum as its timing device. The clock is correct at noon. The next day, when the clock reads noon, the actual time is 11:50 a.m. What is the fractional change in pendulum length that must be made so the clock runs at the correct rate

Answer 1

Answer: the length of the pendulum should be 1.4% longer

Explanation:

Given that;

when its noon, the clock reads 11:50 am,

i.e we have 10 minutes delay ⇒ 10min × 60 = 600secs

we know that in simple pendulum

T = 2π√(l/g)  

d means delay and c means correct;

24hrs = 86400 secs

Now

Td/Tc = (86400-600) / 86400  = 0.993 = [2π√(ld/gc)] / [2π√(ld/gc)] = √(ld/lc)

so ld/lc = 0.98616  

lc = 1.014 ld

lc/l.d = -1 + 1.014 = 0.014 × 100 = 1.4% longer

therefore the length of the pendulum should be 1.4% longer