A hemispherical bowl of radius `R=0.1m` is rotating about its own axis (which is verticle) with an angular velocity `omega`. A particle of mass `10^(-2)kg` on the smooth inner surface of the bowl is also rotating with the same `omega`. The particle is at a height `h` from the bottom of the bowl (a) obtain the relation betweemn `h` and `omega`. what is the minimum value of `omega` needed, in order to have a non-zero value of `h`? (b) it is desired to measure `g` using this set up, by measuring `h` accurately. assuming that `R` and `Omega` are known precisely and least count in the measurement of `h` is `10^(-4)m`, what is the minimum possible error `Deltag` in the measured value of `g`? `(g=10m//s^(2))`

Options

A. `h=omega^(2)/g`
B. `h=R/2`
C. `h=R-g/omega^(2)`
D. None

Answer

C

Explanation

`N sintheta=momega^(2)r=momega^(2)Rsintheta`
`:.N=momega^(2)R, Ncostheta=mg`
`:.cos theta =g/(Romega^(2)),R-h/R=g/Romega^(2)`
`:.h=R-g/omega^(2)`