A grandfather clock uses a pendulum of length \"I\" with a weight of 0.5 attache

Question

  A grandfather clock uses a pendulum of length "I" with a weight of 0.5 attached to the end, to oscillate with a period of T=I sec. The pendulum swings through an angle %u03B8 =10 deg   

A-how long is the pendulum in feet?

B-In operation, the grandfa ther clock is found to show that 24 hours ,0 min ,and 24sec.           Have elapsed in 24 hours. Should u shorten the pendulum, lengthen the pendulum, add more weight , or take a way weight ,to make the clock show the correct time elapsed and how much should you increase or decrease ?

C-if the same pendulum is adjusted to swings through %u03B8=2 deg , what will the period of oscillation of the pendulum be ?   

Explanation / Answer

let L be the length of the pendulum clock

we know that

S = L x theta

or L = (S/theta)

where S is the arc length made by the pendulum and theta = 10o = 10 x (pi/180) radians

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