Two stars of masses `3 xx 10^(31)` kg each, and at distance `2 xx 10^(11)` m 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 Graviational constant `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`)

Options

A. `2.4xx10^4` m/s
B. `3.8xx10^4` m/s
C. `1.4xx10^5` m/s
D. `2.8xx10^5` m/s

Answer

D

Explanation

`1/2mv^2=(2GMm)/R rArr v=sqrt(12xx10^20xx6.67xx10^(-11)) =2.82xx10^5` m/s