An object is dropped from height `h=2 R` on the surface of earth. Find the speed with which it will collide with ground by neglecting effect of air. (Where R is radius of earth, take mass of earth M)

Explanation

To find the speed with which an object dropped from a height \( h = 2R \) will collide with the ground, we can use the principle of conservation of energy. Here’s a step-by-step solution:

### Step 1: Define the Initial and Final Potential Energy
The initial height of the object is \( h = 2R \) above the Earth's surface. Therefore, the total distance from the center of the Earth to the object is \( 3R \) (since the radius of the Earth is \( R \)).

The gravitational potential energy (U) at a distance \( r \) from the center of the Earth is given by the formula:
\[
U = -\frac{GMm}{r}
...