Four beads each of mass `m` are glued at the top, bottom and the ends of the horizontal diameter of a ring of mass`m`. If the ring rolls without sliding with the velocity `v` of its, the kinetic energy of the system (beads+ring) is

Options

A. `5 mv^(2)`
B. `4 mv^(2)`
C. `2mv^(2)`
D. `mv^(2)`

Answer

A

Explanation

`1/2m[4v^(2)+(sqrt(2)v)^(2)+(sqrt(2)v)^(2)+0^(2)]+1/2mv^(2)+1/2Iomega^(2)=1/2m[4v^(2)+4v^(2)]+mv^(2)=5mv^(2)`