Question

A block is tied to a string of length 98 cm and is rotated in a horizontal circle. Find the angular velocity if the centripetal acceleration \( a = g \).

• A. \( \omega = \sqrt{g} \)
• B. \( \omega = \frac{g}{R} \)
• C. \( \omega = \sqrt{g/R} \)
• D. \( \omega = \frac{g}{\sqrt{R}} \)

Hint:

To find the angular velocity when the centripetal acceleration is known, use the relationship \( a_c = R \omega^2 \) and solve for \( \omega \).

Answer 1

The Correct Option is C

We are given that the block is rotating in a horizontal circle, and the centripetal acceleration is equal to \( g \), the acceleration due to gravity. ### Step 1: Formula for Centripetal Acceleration The centripetal acceleration \( a_c \) of an object moving in a circle of radius \( R \) with angular velocity \( \omega \) is given by: \[ a_c = R \omega^2 \] ### Step 2: Set Centripetal Acceleration Equal to \( g \) We are told that the centripetal acceleration is equal to \( g \), so: \[ g = R \omega^2 \] ### Step 3: Solve for Angular Velocity \( \omega \) Solving for \( \omega \), we get: \[ \omega = \sqrt{\frac{g}{R}} \] Thus, the correct answer is: \[ \boxed{(C) \, \omega = \sqrt{\frac{g}{R}}} \]