The linear velocity of a point on the equator is nearly (radius of the earth is 6400 km)

The correct answer is 1600 km/hr.

Step-by-Step Explanation:

1. Understand the Physical Scenario:
The Earth rotates on its axis once every 24 hours. A point on the equator moves in a circle whose radius is equal to the radius of the Earth. We want to find the linear velocity (speed) of this point.

2. Recall the Formula for Linear Velocity:
The linear velocity ($v$) of an object moving in a circle is given by the distance covered in one complete rotation (the circumference of the circle) divided by the time period of one rotation ($T$):

$v=\frac{2\pi R}{T}$

where:
- $R$ is the radius of the circular path (radius of the Earth = 6400 km)
- $T$ is the time period of one rotation (24 hours)
- $\pi$ is approximately 3.14159

3. Substitute the Values into the Formula:

$v=\frac{2\times 3.14159\times 6400\text{km}}{24\text{hr}}$

4. Simplify the Expression:
Let us simplify the fraction:

$v=\frac{6.28318\times 6400}{24}\text{km/hr}$

Dividing 6400 by 24:

$\frac{6400}{24}\approx 266.67$

Now, multiply by 2$\pi$ (approx. 6.283):

$v\approx 6.28318\times 266.67\approx 1675.5\text{km/hr}$

5. Conclusion:
The calculated speed is approximately 1676 km/hr. Comparing this value with the given options, the closest approximate value is 1600 km/hr.