A pendulum having a bob of mass m hangs in a ship that is sailing along the equator from east to west. When the ship is stationary with respect to the water, the tension in the string is T₀ . The angular speed of the earth's rotation is and the radius of the earth is R . Determine the magnitude of the difference between T₀ and the earth's attraction on the bob.

Step-by-step solution

When the ship is stationary with respect to the water, it is at rest relative to the Earth. The bob moves in a circular path of radius R along with the Earth, rotating with angular speed . The forces acting on the bob are the true gravitational attraction of the Earth F_g directed towards the center of the Earth, and the tension in the string T₀ directed away from the center. The net force provides the necessary centripetal acceleration for the circular motion of the bob: F_g - T₀ = m ^2 R The magnitude of the diff