Q.

Two planets A and B of masses  mA and mB are considered fixed in space at separation d. The speed with which a body of mass m is to be projected from the midpoint of the line joining A and B so that the body will escape to infinity is nGmA+mBd. Find the value of n.

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answer is 4.

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Detailed Solution

Due to planets A and B, gravitational potential at mid point V0=-GmAd/2-GmBd/2For body projected from O to escape to infinity TE≥0 12mv2+mv0≥0 12v2+v0≥0 12v2-GmAd/2-GmBd/2≥0  v≥4GmA+mBd ∴ n=4
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