Masses and radii of Earth and Moon are M 1 , M 2 and R 1 , R 2 respectively. The distance between their centre is 'd'. The minimum velocity given to mass 'M' from the mid p

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Masses and radii of Earth and Moon are M 1 ​ , M 2 ​ and R 1 ​ , R 2 ​ respectively. The distance between their centre is 'd'. The minimum velocity given to mass 'M' from the mid point of line joining their centre so that it will escape :-

TestHub · Accepted Answer

At the midpoint, the mass M is at distance d/2 from each centre. To escape, its kinetic energy must equal the total potential energy there: $\frac{1}{2} M v^{2} = \frac{G M _{1} M}{d /2} + \frac{G M _{2} M}{d /2}$ .

So $v^{2} = \frac{4 G ( M _{1} + M _{2} )}{d}$ , giving $v = \frac{4 G ( M _{1} + M _{2} )}{d}$ .

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