If radius of the earth is doubled without change in its mass, what will be the length of the day?

Explanation

To solve the problem of finding the new length of the day if the radius of the Earth is doubled while keeping its mass constant, we can follow these steps:

### Step 1: Understand the relationship between radius and angular velocity
The Earth rotates about its axis, and the length of the day is determined by the time it takes for one complete rotation. The angular velocity (ω) of the Earth is related to the gravitational force and the radius of the Earth.

### Step 2: Use the formula for gravitational force
The gravitational force (F) acting on an object at the surface of the Earth is given by:
\[ F = \frac{G \cdot M}{R^2} \]
...