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Two states each of one solar mass (2xx10...

Two states each of one solar mass `(2xx10^(30)kg)` are approaching each other for a head on collision. When they are at a distance `10^(9)` their speeds are negotiable. What is the speed with which they collide ? The radius of each star is `10^(4)` assume the stars to remain undistorted unit thye collide.

Text Solution

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`m_(1)=m_(2)=2xx10^(30)kg,d=10^(9)km=10^(12)m,r_(1)=r_(2)=10^(7)m`
Applying `(Gm_(1)m_(2))/(d) =1/2m_(1)v^(2)`
we get `v = sqrt((2Gm_(2))/(d))=sqrt((2xx6.67xx10^(-11)xx2xx10^(30))/(10^(12)))`
`v = 16.33xx10^(3)ms^(-1)`
ie., `v=16.3kms^(-1)`
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