Physics

Physics

Problem

A planet has mass MM and radius RR. A tunnel is dug deep into the planet such that the bottom is at a distance r=R/2r = R/2 from the center. A particle is launched from the bottom of this tunnel. Given that the potential inside a uniform sphere is V(r)=−GM(3R2−r2)2R3V(r) = -\frac{GM(3R^{2} - r^{2})}{2R^{3}}, find the escape velocity.

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