Two uniform spheres A (Hollow) and B (solid) of same radius R (

Options

A. Mg
B. `(Mg)/(5(R^(2)+2r^(2)))xx3(R^(2)+6r^(2))`
C. `(4Mg)/(5(R^(2)+2r^(2)))xxR^(2)`
D. `(Mg)/(5(R^(2)+2r^(2)))xx4R^(2)`

Answer

A

Explanation

From `tau=Ialpha`

`Mgxxrcos37^@=[(MR^(2))/2+Mr^(2)]alpha`
`alpha=(8rg)/(5[R^(2)+2^(2)])`
From energy conservation
`(Iomega^(2))/2=Mgxxrsin37^@`
`[(MR^(2))/2+Mr^(2)](omega^(2))/R=Mgrxx3/5`
`omega=sqrt((12gr)/(5[R^(2)+2r^(2)]))`
For `FBD` of the disc
`R_(x)-mgsin37^@=Ma_(r)=momega^(2)r`

`Mgcos37^@-R_(y)=Ma_(t)=Mralpha`
`R_(x)=(3Mg)/5[(R^(2)+6r^(2))/(R^(2)+2r^(2))], R_(y)=(Mg)/5[(4R^(2))/(R^(2)+2r^(2))]`
`R=sqrt(R_(x)^(2)+R_(y)^(2))=(Mg)/(5[R^(2)+2r^(2)])xxsqrt(9(R^(2)+6r^(2))^(2)+(4R)^(2))`