If a particle of mass z is projected with minimum velocity from the surface of a star with kinetic energy $$K1GMm/a$$ and potential energy at surface of the star $$K2GMm/a$$ towards the star of same mass m and radius a (K1$$ and $$K2$$ are $$constants) to reach the other star. Find the distance between the centre of the two stars

Question

If a particle of mass z is projected with minimum velocity from the surface of a star with kinetic energy $$K1GMm/a$$ and potential energy at surface of the star $$K2GMm/a$$ towards the star of same mass m and radius a (K1$$ and $$K2$$ are $$constants) to reach the other star. Find the distance between the centre of the two stars

Infinity Learn · Accepted Answer

Since the mass and radius of two stars are same, point P at which gravitational force will be equal, will be at equal distance (say$$ $$r) from centre of each star. The particle should be projected to cross P, beyond which the particle will be attracted towards the other star.$$KE$$ $$=$$ $$PE$$ of body at $$P-$$ P at surface of the $$starK1GMma=$$−GMmr−GMmr−−$$K2GMmaon$$ solving, $$r=2aK2$$−$$K12$$ $$r=4aK2$$−$$K1$$

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