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The masses and radii of the Earth and th...

The masses and radii of the Earth and the Moon are `M_1, R_1 and M_2,R_2` respectively. Their centres are at a distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

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Verified by Experts

The correct Answer is:
`sqrt((4G)/d(M_1+M_2))`
To escape to infinity , `V_oo=0^+` Applying energy conservation for the particle.
`DeltaU+DeltaK=0 " " 0-m(-(GM_1)/(d//2)-(GM_2)/(d//2))+0-1/2m u^2=0 rArr u=sqrt((4G)/d(M_1+M_2))`
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