Two starts each of one solar mass `(=2xx10^(30)kg)` are approaching each other for a head on collision. When they are a distance `10^(9)`km. their speeds are negligible. What is the speed with which they collide? The radius of each star is `10^(4)`km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Explanation

To solve the problem of two stars colliding, we will use the principle of conservation of energy. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Initial Conditions
- Each star has a mass \( M = 2 \times 10^{30} \) kg (solar mass).
- The initial distance between the centers of the two stars is \( R = 10^9 \) km, which we convert to meters:
\[ R = 10^9 \text{ km} = 10^{12} \text{ m} \]
...