Question

Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds \(v_p\), \(v_q\), and \(v_r\), respectively.
Which one of the following options is CORRECT?

• A. \(v_p < v_r < v_q\)
• B. \(v_p < v_q < v_r\)
• C. \(v_p > v_r > v_q\)
• D. \(v_p = v_r \neq v_q\)

Hint:

For rotating objects, the speed of any point is directly proportional to its distance from the axis of rotation. Points near the axis (like the poles) move slower than points farther away (like the equator).

Answer 1

The Correct Option is C

We are given a rotating spherical globe with three points: P on the equator, Q at the north pole, and R midway between the equator and the north pole. The points P, Q, and R move with speeds \(v_p\), \(v_q\), and \(v_r\), respectively.
To understand the movement of these points, we must recognize that the rotational speed of any point on the globe depends on its distance from the axis of rotation. The equator is farthest from the axis, while the poles are at the axis, leading to different speeds.
1. At point P (the equator): The rotational speed is the greatest because the equator is at the maximum distance from the axis. The speed is proportional to the radius of the Earth, so \(v_p\) is the highest.
2. At point Q (the north pole): The rotational speed is zero because point Q lies directly on the axis of rotation. Hence, \(v_q = 0\).
3. At point R (midway between the equator and the north pole): The rotational speed at point R is less than at the equator but greater than at the north pole. Therefore, \(v_r\) lies between \(v_p\) and \(v_q\).
Since \(v_p > v_r > v_q\), the correct answer is option (C).