A uniform solid cone of mass m, base radius ‘R’ and height 2R, has a smooth groove along its slant height as shown in figure. The cone is rotating with angular speed `omega`, about the axis of symmetry. If a particle of mass ‘m’ is released from apex of cone, to slide along the groove, then angular speed of cone when particle reaches to the base of cone is

Options

A. `(3 omega)/13`
B. `(4 omega)/13`
C. `(5 omega)/13`
D. `( 9 omega)/13`

Explanation

Initially
`I_(1)=3/10 mR^(2) & omega_(1)=omega`
Finally `I_(2) =13/10 mR^(2)& omega_(2)=omega_("new")`
Using conservation of anular momentum
`I_(1)omega_(1)=I_(2)omega_(2)`
`omega_(2)=omega_("new")=(3omega)/13`