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The small sphericla balls are free to mo...

The small sphericla balls are free to move on the inner surface of the rotating spherical chamber of radius `R=0.2 m` If the balls reach a steady at angular position `theta=45^(@)`, the anglular speed `omega` of devices is

A

`8 rad//s`

B

`2 rad//s`

C

`3.64 rad//s`

D

`9.34 rad//s`

Text Solution

Verified by Experts

(c) Here, R`=0.2 m`

From figure `r=3R+Rsin45^(@)`
In the fram of rotating spherical chamber (n0n-inertial)
`Ncos45^(@) =mromega^(2)`
`N sin 45^(@) -mg`
Dividing Eq. (ii) by Eq(i), we get
`:." " tan45^(@)=(mg)/(mromega^(2))=(g)/(romega^(2))`
`:." " omega=sqrt((g)/(r))=sqrt(((g)/(3R+R/sqrt(2))))=3.64 rad//s`
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