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Because of the rotation of the Earth, a plumb bob may not hang exactly along the direction of the Earth's gravitational force on the plumb bob but may deviate slightly from that direction. (a) Show that the deflection θ in radians at a point at latitude L is given by Where R is the radius of the Earth and T is the period of the Earth’s rotation. (b) At what Latitude is the deflection a maximum? How much is this deflection? (c) What is the deflection at the poles? At the equator?

Because of the rotation of the Earth, a plumb bob may not hang exactly along the direction of the Earth's gravitational force on the plumb bob but may deviate slightly from that direction. (a) Show that the deflection θ in radians at a point at latitude L is given by
                        
Where R is the radius of the Earth and T is the period of the Earth’s rotation. (b) At what Latitude is the deflection a maximum? How much is this deflection? (c) What is the deflection at the poles? At the equator?

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
(a)
The centripetal force experienced by the bob is given as:
236-1157_1.PNG
Here, T is the time period of Earth.
Also, the radius x can be related to the radius of the Earth as:
236-770_1.PNG
Use Newton’s law for the forces lying along the line joining the bob and the center of Earth (refer figure above),

236-199_1.PNG
236-959_1.PNG
Similarly, use Newton’s second law of motion for the forces horizontal to the Earth’s surface,

236-2103_1.PNG
236-993_1.PNG
236-1478_1.PNG
Therefore, the maximum angular displacement of the plumb bob is 1.7 x 10-3 rad.
236-1761_1.PNG

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