Answer
Given,
Period of the Pendulum, T= 1 s
acceleration due to gravity, g = 9.8 m/s²
Length of Bob = 0.2482 m
Loss of time in the clock = 1.5 minutes/ day
Loss of time in 1 oscillation
= [tex] \dfrac{1.5\times 60}{24\times 60\times 60}[/tex]
= 0.001042
Hence, time period, T = 1 + 0.001042
T = 1.001042 s
a) Using Time period of oscillation formula
[tex]T = 2\pi \sqrt{\dfrac{L}{g}}[/tex]
[tex]1.001402 = 2\pi \sqrt{\dfrac{0.2482}{g'}}[/tex]
[tex] g' = 9.77\ m/s^2[/tex]
Free fall acceleration at the clock location = 9.77 m/s²
b) Length of pendulum bob to keep it perfect time
[tex]1 = 2\pi \sqrt{\dfrac{L}{g}}[/tex]
[tex]1 = 2\pi \sqrt{\dfrac{L'}{9.77}}[/tex]
[tex]L' = 0.2475\ m[/tex]
Hence, Length of pendulum bob is equal to 0.2475 m.
