Question

Two stars each of one solar mass (= 2 x 10³⁰ kg) are approaching each other for a head on collision. When they are a distance 10⁹ km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 10⁴ km. Assume the stars to remain undistor-ted until they collide.(Use the known value of G).

Answer 1

Mass of each star, M = 2 x 10³⁰ kg

Initial distance between two stars = r

= 10⁹ km = 10¹² m

Initial P.E. of the system = -GMM/r

Total K.E. of the stars = 1/2Mv² + 1/2Mv² = Mv²

where v is the speed of collision of stars. Just before they are colliding, the distance between their centres = 2R

Hence, final P.E. of the system = -GMM/2R

Gain in K.E. is at the cost of loss in P.E.

We have,