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Distance between the centres of two star...

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

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The correct Answer is:
`(3)/(2)sqrt((5GM)/(a))`

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))`
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