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Chapter 4: Problem 120

By what percentage does the weight of an object change when it is moved from the equator at sea level, where the effective value of \(g\) is $9.784 \mathrm{N} / \mathrm{kg},\( to the North Pole where \)g=9.832$ N/kg?

Short Answer

Expert verified
Answer: The approximate percentage change in weight of an object when it is moved from the equator to the North Pole is 0.49%.

Step by step solution

01

Identify the given values

The value of \(g\) at the equator is given as \(g_{equator} = 9.784\,\mathrm{N/kg}\). At the North Pole, the value of \(g\) is given as \(g_{northpole} = 9.832\,\mathrm{N/kg}\).
02

Calculate the change in weight due to the change in \(g\) values

The change in weight, \(\Delta Weight\), can be calculated by subtracting the weight due to \(g_{equator}\) from the weight due to \(g_{northpole}\). Since the mass of an object does not change depending on its location, we can focus on the change in \(g\) values only: \(\Delta g = g_{northpole} - g_{equator} = 9.832\,\mathrm{N/kg} - 9.784\,\mathrm{N/kg} = 0.048\,\mathrm{N/kg}\)
03

Calculate the percentage change in weight

To calculate the percentage change in weight, we can use the following formula: \(Percentage\,Change = \frac{\Delta g}{g_{equator}} * 100\) Plug in the values: \(Percentage\,Change = \frac{0.048\,\mathrm{N/kg}}{9.784\,\mathrm{N/kg}} * 100\)
04

Compute the result

Calculate the percentage change: \(Percentage\,Change \approx 0.4904 \%\) The weight of an object changes by approximately \(0.49 \%\) when it is moved from the equator to the North Pole.

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