A solid disk rotates in the horizontal plane at an angular velocity of `0.067 "rad"//s` with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is `0.10 kg.m^(2)`. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

Options

A. `0.067 "rad"//s`
B. `0.046 "rad"//s`
C. `0.059 "rad"//s`
D. `0.037 "rad"//s`

Answer

D