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2 uniform spheres of equal radii R ,but mass M and 4M have a center to center separation 6R.the 2 spheres are held fixed .A projectile of mass m is projected from the surface of sphere of mass M directly towards the center of the second one .Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of second one.



The neutral point r = – 6R does not concern us in this example. Thus ON = r = 2R. It is sufficient to project the particle with a speed which would enable it to reach N. Thereafter,the greater gravitational pull of 4M would suffice. The mechanical energy at the surface of M is

At the neutral point N, the speed approaches zero. The mechanical energy at N is purely potential.


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