Question

A particle is projected from the surface of one star towards other star of same radius `a` and mass with such a minimum velocity`Ksqrt((GM)/a)`, so that it is attracted towards other star. Find the value of `K` if two stars are `2r` distance apart:

A. `(2(r-a))/([r(2r-a)]^(1//2))`
B. `(2(r-a))/([r(r-a)]^(1//2))`
C. `(r-a)/([r(r-a)]^(1//2))`
D. `(r+a)/([r(r-a)]^(1//2))`

Answer 1

Correct Answer - A
`1/2mv_(min)^(2)=[-(GMm)/r-(GMm)/r]`
`-[-(GMm)/((2r-a))-(GMm)/a]`
`=(2GMm(a^(2)-2ar+r^(2)))/(ar(2r-a))`
or `v_(min)=sqrt((GM)/a)xx(2(r-a))/([r(2r-a)]^(1//2))`
So, `K=(2(r-a))/([r(2r-a)]^(1//2))`