Question

Two starts each of one solar mass `(=2xx10^(30)kg)` are approaching each other for a head on collision. When they are a distance `10^(9)`km. their speeds are negligible. What is the speed with which they collide? The radius of each star is `10^(4)`km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Answer 1

Here, mass of each star, `M=2xx10^(30)kg`
Initial potential between two stars, `r=10^(9)km=10^(12)m`
Initial potential energy of the system=`-GMm//r`
Total K.E. of the stars `=1//2MV^(2)+1//2Mv^(2)`
Where v is the speed of stars with which they collide when the stars are about to collide, the distance between their centres, r=2R.
`therefore` Final potential energy of two stars=GMm/2R
Since gain in K.E. is the cost of loss in PE