Question

Tamsen is interested in history, and read that because of its regular period, the pendulum constituted the basis of the most accurate clocks for nearly 300 years. 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.
Vera and Tamsen discuss how much shorter the SI unit of length, the meter, would have had to be had Huygens' suggestion been followed.
Which of their conclusions is correct?

a) 0.025 m b) 0.752 m c) 0.248 m d) 1.56 m

Answer 1

We will apply the concept of period in a pendulum, defined as the product between 2$\pi$ by the square root of the length over gravity, this is mathematically

$T = 2\pi \sqrt{\frac{L}{g}}$

Here,

T = Period

L = Length

g = Acceleration due to gravity

For the period to be 1 second, then we must look for the necessary length for such a requirement so

$1 = 2\pi \sqrt{\frac{L}{9.8}}$

$(\frac{1}{2\pi})^2 = \frac{L}{9.8}$

$L = 9.8(\frac{1}{2\pi})^2$

$L = 0.2482m$

The meter's length would be slight less than one-fourth of its current length. Also, the number of significant digits depends only on how precisely we know g, because the time has been defined to be exactly 1s.

Therefore the correct answer is C.