A uniform solid sphere has mass M and radius R. A narrow tunnel is drilled through its centre. A particle is released from rest at the surface. Its speed at the centre is:
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A uniform solid sphere has mass M and radius R. A narrow tunnel is drilled through its centre. A particle is released from rest at the surface. Its speed at the centre is:

G1 Physics · Accepted Answer

For a uniform sphere, V_surface=−GM/R and V_centre=−3GM/(2R). Energy conservation gives ½mv²=m(V_surface−V_centre)=GMm/(2R), so v=√(GM/R).