Sara and Meg are on a merry-go-round Sara is sitting closer to the outside of the merry-go-round (radius=5m) while Meg chose a horse on the inside of the ride (radius=3m) Both girls have the same mass of 80 kg.Sara's tangential velocity is 3.4m/s and Meg's tangential velocity is 2.1m/s Which girl has the larger centripetal force? Sara They are equal. Meg Not enough information to determine.

## Step 1The problem involves the concept of centripetal force, which is the force that keeps an object moving in a circular path. The centripetal force is given by:### where is the centripetal force, is the mass of the object, is the velocity of the object, and is the radius of the circular path.## Step 2In this problem, both Sara and Meg have the same mass ( ), but different velocities ( for Sara and for Meg) and different radii ( for Sara and for Meg).## Step 3We can calculate the centripetal force for each girl using the formula from Step 1.For Sara, the centripetal force is:### \(F_{Sara} = \frac{80kg \times (3.4m/s)^2}{5m} = 231.2 N\)For Meg, the centripetal force is:### \(F_{Meg} = \frac{80kg \times (2.1m/s)^2}{3m} = 56.8 N\)## Step 4Comparing the two forces, we can see that Sara's centripetal force is greater than Meg's.