Gravitation 5 Question 3
3. Two stars of masses each and at distance rotate in a plane about their common centre of mass . A meteorite passes through 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 is (Take, gravitational constant, ) (Main 2019, 10 Jan II)
(a)
(b)
(c)
(d)
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Answer:
Correct Answer: 3. (a)
Solution:
- Let us assume that stars are moving in
-plane with origin as their centre of mass as shown in the figure below
According to question, mass of each star,
Potential energy of meteorite at
If
To escape from this dual star system, total mechanical energy of the meteorite at infinite distance from stars must be at least zero. By conservation of energy, we have