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Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

1. Decrease the amplitude of swing by a small amount.
2. Remove some mass from the weight.
3. Lower the weight.
4. Raise the weight.
5. Add more mass to the weight.

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Answer:

3. Lower the weight.

Explanation:

The time period of a pendulum is given by

[tex]T=2\pi\sqrt{\dfrac{L}{g}}[/tex]

where,

L = Length of pendulum

g = Acceleration due to gravity = 9.81 m/s²

It can be seen from the equation that the time period depends on the length of the pendulum and the acceleration due to gravity of the planet.

The acceleration due to gravity of the planet is constant so the time period is proportional to the length of the pendulum.

[tex]T\propto \sqrt{L}[/tex]

Here, the time period has reduced as the clock runs fast.

So, in order to increase the time period we have to lower the weight.

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