Question

On earth, prospectors are looking for a deposit of iron ore beneath the ground. They decide to use the acceleration of gravity to find where the iron is located because the additional iron mass should change the acceleration of gravity. They use a carefully-made pendulum with a length of 2.00000 meters and measure the period of the swing as they walk around the area where they think the deposit is located. To the nearest millionth of a second, how much will the period change if the acceleration of gravity between two spots changes from 9.80000 meters/sec2 to 9.80010 meters/sec2?

Answer 1

To calculate the change in the period of a pendulum due to a slight change in the acceleration due to gravity, we use the period formula for a simple pendulum. The very small change in gravity causes a correspondingly small change in the period, signifying the sensitivity of pendulum measurements.

Step-by-step explanation:

The question involves using the properties of a pendulum to measure changes in the acceleration due to gravity (g). The formula for the period (T) of a simple pendulum is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If g changes from 9.80000 m/s² to 9.80010 m/s², we can use this formula to calculate the change in the period to the nearest millionth of a second.

First, calculate the initial period using the given g value and the length of the pendulum:

T₁ = 2π√(2.00000 m / 9.80000 m/s²) = 2.00000 s (since it is given that the pendulum originally had a period of 2 seconds).

Next, calculate the new period using the slightly altered value of g:

T₂ = 2π√(2.00000 m / 9.80010 m/s²).

Upon solving, you will find that the period decreases by a very small amount, demonstrating the sensitivity of the pendulum to changes in acceleration due to gravity.