Let `P` be the point on the line joining the centre of the two plantes s.t the net field at it is zero
Then `(GM)/(r^(2)) (G. 16M)/((10a -r)^(2)) =0 rArr (10 a-r)^(2) = 16r^(2)`
`rArr 10a-r = 4r rArr r =2a`
Potential at point P `v_(P) = (-GM)/(r) - (G.16M)/((10a -r)) = (-GM)/(2a) - (2GM)/(a) = (-5GM)/(2a)`
Now if the particle projected from the larger planet has enough energy to cross this point it will reach the smaller planet For this the `K.E` imparted to the body must be just enough to raise its total mechnical energy to a value which is equal to `P.E` at point `P`
`(1)/(2)mv^(2) - (G (16M)m)/(2a) (-GMm)/(8a) =mv_(P)`
or `(v^(2))/(2) (-8GM)/(a) (-GM)/(8a) = (-5GMm)/(2a)`
or `v^(2) = (45GM)/(4a)` or `v_(min) = (3)/(4) sqrt((5GM)/(a))`
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