A uniform solid sphere of mass M and radius R has a narrow diametric tunnel. A particle released from rest at the surface reaches the centre with speed:
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A uniform solid sphere of mass M and radius R has a narrow diametric tunnel. A particle released from rest at the surface reaches the centre with speed:

G1 Physics · Accepted Answer

V_surface=−GM/R and V_centre=−3GM/(2R). Energy conservation: ½mv²=m(V_surface−V_centre)=GMm/(2R), hence v=√(GM/R).