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 solve the problem of finding the speed of an object dropped from a height of \( h = 2R \) (where \( R \) is the radius of the Earth) when it collides with the ground, we can use the principle of conservation of mechanical energy. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Initial and Final States
- The object is dropped from a height of \( h = 2R \) above the Earth's surface. Therefore, the total height from the center of the Earth is \( h + R = 3R \).
- At the initial position (height \( 2R \)), the object has potential energy and no kinetic energy since it is dropped from rest.

### Step 2: Write the Conservation of Mechanical Energy Equation
- According to the conservation of mechanical energy:
...