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A compound sphere is made by joining a h...

A compound sphere is made by joining a hemispherical shell and a solid hemisphere of same radius `R` and same mass as shown in figure. This system is kept between two smooth parallel walls and a smooth floor with the hollow hemisphere on the top as shown in figure. The maximum angular velocity of the compound shere when the system is slightly disturbed is `(` all surfaces are smooth `)`

A

`sqrt((15g)/(64R))`

B

`sqrt((15g)/(32R))`

C

`sqrt((15g)/(16R))`

D

`sqrt((15g)/(8R))`

Text Solution

Verified by Experts

The correct Answer is:
B
Change in `PE=` Increase in `K.E.`
`Mg[(R)/(2)2-(3R)/(8)2]=(1)/(2)[(2)/(5)MR^(2)+(2)/(3)MR^(2)]omega^(2)(g)/(4)`
`=(2)/(2)[(1)/(5)+(1)/(3)]Romega^(2) sqrt((15g)/(32R))=omega`
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