Christian Huygens (1629-1695), the greatest clockmaker in history, suggested tha

Question

Christian Huygens (1629-1695), the greatest clockmaker in history, suggested that an international unit of length could be defined as the length of a simple pendulum having a period of exactly 1 s. How much shorter would our length unit be if his suggestion had been followed?

A grandfather clock is found to gain 22.0 s every 24 hours. If the current length of the pendulum is 0.750 m, how much should the length be changed to make the clock accurate? Let a positive value correspond to an increase in length, and a negative value correspond to a decrease.
?L = m

Explanation / Answer

1 =2*3.14(l/g)

g =9.81

hence length unit =l =0.248 m

ie 0.248 th times meter unit

.......

22 s in 24 hrs

ie 2.55*10^-4 sec in a sec

hence T =2*3.14*(0.75/9.8) = 1.7373 sec

T' should be 1.7373+0.000255

hence new length =9.8*T'/(4*3.14^2)

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