To decrease the period of the pendulum, B) Make the pendulum slightly shorter. --> TRUE
Explanation:
The period of a simple pendulum is given by the equation:
![T=2\pi \sqrt{\frac{L}{g}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%7D)
where
L is the length of the pendulum
g is the acceleration of gravity
We notice that the period of a pendulum does not depend on the mass hanging on the pendulum, but only on its length. We also notice that:
- The period is proportional to the square root of the length of the pendulum, ![T\propto \sqrt{L}](https://tex.z-dn.net/?f=T%5Cpropto%20%5Csqrt%7BL%7D)
- The period is inversely proportional to the square root of the acceleration of gravity, ![T \propto \frac{1}{\sqrt{g}}](https://tex.z-dn.net/?f=T%20%5Cpropto%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bg%7D%7D)
Here we want to decrease the period of the pendulum, from 2.0 s to 1.9 s. Now we can analyze the four options:
A) Remove some mass from the pendulum. --> FALSE. The period does not depend on the mass.
B) Make the pendulum slightly shorter. --> TRUE. Decreasing the length, L, will also decrease the period.
C) Add more mass to the pendulum. --> FALSE. The period does not depend on the mass.
D) Make the pendulum slightly longer. --> FALSE. Increasing the length, L, will also increase the period.
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