Question

A hemispherical bowl of radius R = 0.1 m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass10⁻² kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at height h from the bottom of the bowl. 

(a) Obtain the relation between h and ω. What is the minimum value of ω needed, in order to have a nonzero value of h? 

(b) It is desired to measure (acceleration due to gravity) using the setup by measuring h accurately. Assuming that R and ω are known precisely and that the least count in the measurement of h is 10^-4 m, what is minimum possible error ∆g in the measured value of g?

Answer 1

Given : R = 0 1m, m = 10^–2 kg

(a) FBD of particle in ground frame of reference is shown in figure. Hence,

Therefore, minimum value of ω should be

(b) Eq. (iii) can be written as h = \(R -\frac g{\omega^2}\)

If R and ω are known precisely, then

Answer 2

Answer is :

(a) 9.89 rad/sec, 

(b) 9.8 \(\times\) 10^-3 m/s²