Because of the Earth's rotation, a plumb bob does not hang exactly along a line directed to the center of the Earth. How much does the plumb bob deviate from a radial line at 35.1° north latitude? Assume the Earth is spherical.

To determine the deviation of the plumb bob from a radial line at a specific latitude, we need to understand the concept of the Earth's rotation and its effect on gravity.

The Earth's rotation creates a centrifugal force that causes an apparent deviation in the direction of gravity. This deviation is known as the "deflection of the vertical" and causes the plumb bob to hang slightly off-center instead of along a line directed to the center of the Earth.

Fortunately, we can use a mathematical formula called the "formula of Earth's rotation" to calculate the deviation. The formula is given by:

d = (2 * Ω * sin(φ)) / g

Where:
- d is the deviation of the plumb bob from the radial line
- Ω is the angular velocity of the Earth's rotation (approximately 7.2921159 × 10^-5 radians/second)
- φ is the latitude in radians
- g is the acceleration due to gravity (approximately 9.8 m/s²)

First, we need to convert the latitude from degrees to radians.
φ = (35.1° * π) / 180° = 0.612 radians

Next, we can substitute the values into the formula:
d = (2 * 7.2921159 × 10^-5 * sin(0.612)) / 9.8

After performing the necessary calculations, we find that the plumb bob deviates from a radial line by approximately 0.005898 meters (or 5.898 millimeters) at 35.1° north latitude.