Final answer:
To find the angular velocity in a bowl, we set the centripetal acceleration equal to gravitational acceleration and solve for ω, resulting in the MCQ answer (D) √(R/g).
Step-by-step explanation:
To solve for the angular velocity in a bowl with a given radius and depth, we must understand the relationship between the angular velocity (ω), the radius (r), and the effect of gravity (g). The formula for angular velocity, ω, can be derived from setting the centripetal acceleration equal to the gravitational acceleration. The relevant formula would be v²/r = g, where v represents the tangential velocity. However, if we wish to find the angular velocity, we have to relate the tangential velocity to angular velocity using the formula v = rω. By substituting into the initial equation, we obtain ω² = g/r. To solve for ω, we would take the square root of both sides, resulting in ω = √(g/r).
The correct MCQ answer in this case is (D) square root R/g.