Distance between the centres of two stars is `10a`. The masses of these stars are `M` and `16 M` and their radit `a` and `2a` respectively. A body of mass `m` is fired straight from the surface of the larger star towards the smaller star. What should be its minimum inital speed to each the surface of the smaller star? Obtain the expression in terms of `G`, `M` and `a`.

Answer

`(3)/(2)sqrt((5GM)/(a))`

Explanation

point P where field is zero
`implies(GMm)/((10a-x)^(2))=(G(16M)m)/(x^(2))impliesx=8a`
COME: `-(G(16M)m)/(2a)-(GMm)/(8a)+(1)/(2)mv^(2)`
`=-(G(16M)m)/(8a)-(GMm)/(2a)impliesv=(3)/(2)sqrt((5GM)/(a))`