A hollow sphere of radius R and mass m is fully filled with non viscous liquid of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls
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A hollow sphere of radius R and mass m is fully filled with non viscous liquid of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls

G1 Physics · Accepted Answer

Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives L = 8mvR/3.