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The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at  a distance ‘r’ apart. Find the minimum escape velocity for a particle of mass ‘m’ to be projected from the middle of these two masses:

Option 1 -

V = 1 2 4 G ( M 1 + M 2 ) r

Option 2 -

V = 4 G ( M 1 + M 2 ) r

Option 3 -

V = 2 G ( M 1 + M 2 ) r

Option 4 -

V = 1 2 2 G ( M 1 + M 2 ) r

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • R

    Answered by

    Raj Pandey | Contributor-Level 9

    2 months ago
    Correct Option - 2


    Detailed Solution:

    at point P,

    = K E P + P E P

    = 1 2 m v P 2 + { − G M 1 m ( r / 2 ) − G M 2 m r / 2 }

    at infinity (ie for escaping from both masses)

    ⇒ v P = 4 G ( M 1 + M 2 ) r

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