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

Explanation

The distance (from the smaller planet) where the gravitational pull of two planet.s balance each other wi be given by
`(-"GMm")/("x"^(2))=(G(16M)m)/((10a-"x")^(2))`
i.e., x=2 a
So, the body will reach the smaller planet due to planet.s gravitational field ifit has sufficient energy to cro
the point B (x = 2a),i.e.,
`(1)/(2)"mv"^(2)gt m(V_(B)-V_(s))`
but `V_(s)=-[(16"GM")/(2a)+("GM")/((10a-2a))]=-(65"GM")/(8a)`
and `V_(B)=-[(16"GM")/(8a)+("GM")/(2a)]=-(20"GM")/(8a)`
So, `(1)/(2)"mv"^(2)gt m[(65"GM")/(8a)-(20"GM")/(8a)]`
i.e., `V_("min")=(3)/(2) sqrt ((5"GM)/(a))`