By conservation of energy, when object falls by a distance of h.\\\\(\\cfrac { 1 }{ 2 } m{ v }^{ 2 }+\\cfrac { 1 }{ 2 } { I }_{ shell }{ \\omega }_{ shell }^{ 2 }+\\cfrac { 1 }{ 2 } { I }_{ pulley }=mgh\\\\)\\\\(v=R\\omega \\\\)\\\\(\\cfrac { 1 }{ 2 } m{ v }^{ 2 }+\\cfrac { 1 }{ 2 } { \\left( \\cfrac { 2 }{ 3 } M{ R }^{ 2 } \\right) }\ imes { \\left( \\cfrac { v }{ R } \\right) }^{ 2 }+\\cfrac { 1 }{ 2 } { I }_{ p }{ \\left( \\cfrac { v }{ { r }_{ p } } \\right) }^{ 2 }=mgh\\\\)\\\\({ v }^{ 2 }\\left( m+\\cfrac { 2 }{ 3 } M+\\cfrac { { I }_{ p } }{ { r }_{ p }^{ 2 } } \\right) =2mgh\\\\)\\\\(v=\\sqrt { \\cfrac { 2mgh }{ \\left( m+\\cfrac { 2 }{ 3 } M+\\cfrac { { I }_{ p } }{ { r }_{ p }^{ 2 } } \\right) } } \\\\)