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N76 [4]
3 years ago
12

A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g 5 9.8

00 m/s2. The pendulum bob has length L 5 0.248 2 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes per day. (a) What is the free-fall acceleration at the clock’s location? (b) What length of pendulum bob is required for the clock to keep perfect time?
Mathematics
1 answer:
mafiozo [28]3 years ago
7 0

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

   = \dfrac{1.5\times 60}{24\times 60\times 60}

   = 0.001042

Hence, time period, T = 1 + 0.001042

                                  T = 1.001042 s

a) Using Time period of oscillation formula

T = 2\pi \sqrt{\dfrac{L}{g}}

1.001402 = 2\pi \sqrt{\dfrac{0.2482}{g'}}

g' = 9.77\ m/s^2

Free fall acceleration at the clock location = 9.77 m/s²

b) Length of pendulum bob to keep it perfect time

 1 = 2\pi \sqrt{\dfrac{L}{g}}

 1 = 2\pi \sqrt{\dfrac{L'}{9.77}}

 L' = 0.2475\ m

Hence, Length of pendulum bob is equal to 0.2475 m.

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