Which of the following statements are true? For a particle on the surface of the earth:

Options

A. the linear speed is minimum at the equator
B. the angular speed is maximum at the equator
C. the linear speed is minimum at the poles
D. the angular speed is `7.3xx10^(-5) rads^(-1)` at the equator

Explanation

To determine which statements are true for a particle on the surface of the Earth, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Statement:** Linear speed is minimum at the equator.

- **Explanation:** The linear speed (v) of a particle on the surface of the Earth is given by the formula:
\[ v = r \omega \]
where \( r \) is the radius of the Earth at the equator and \( \omega \) is the angular speed. Since the radius at the equator is maximum, the linear speed will also be maximum there. Thus, this statement is **false**.

### Step 2: Analyze Option 2
**Statement:** Angular speed is maximum at the equator.

- **Explanation:** Angular speed (\( \omega \)) is defined as the rate of rotation and is constant for all points on the Earth’s surface. Therefore, it does not vary with latitude. Thus, this statement is also **false**.

### Step 3: Analyze Option 3
**Statement:** Linear speed is minimum at the poles.

- **Explanation:** At the poles, the radius \( r \) is effectively zero (since you are at the axis of rotation), leading to:
\[ v = r \omega = 0 \cdot \omega = 0 \]
Therefore, the linear speed is indeed minimum (zero) at the poles. This statement is **true**.

### Step 4: Analyze Option 4
**Statement:** Angular speed is \( 7.3 \times 10^{-5} \) radians per second at the equator.

- **Explanation:** The angular speed can be calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
where \( T \) is the time period of one complete rotation (24 hours). Converting 24 hours into seconds:
\[ T = 24 \times 3600 \text{ seconds} = 86400 \text{ seconds} \]
Thus,
\[ \omega = \frac{2 \times 3.14}{86400} \approx 7.3 \times 10^{-5} \text{ radians/second} \]
Therefore, this statement is **true**.

### Summary of Results:
- Option 1: False
- Option 2: False
- Option 3: True
- Option 4: True