Two stars of masses `3×10^31kg` each, and at distance `2×10^11m` rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is : (Take Gravitational constant `G=6.67×10^−11Nm^2kg^−2`)

Explanation

To find the minimum speed that the meteorite should have at point O in order to escape the gravitational field of the double star system, we can use the concept of gravitational potential energy and kinetic energy.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of each star, \( M = 3 \times 10^{31} \, \text{kg} \)
- Distance between the two stars, \( d = 2 \times 10^{11} \, \text{m} \)
- Gravitational constant, \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
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