A quality test has determined that a pump impeller is too heavy on one

side by an amount equal to 0.0045 kg-m. To correct this imbalance it is

recommended to cut out a groove around the outer circumference of the

impeller, using a milling machine, on the same side as the imbalance.

This will remove material with the intent of correcting the imbalance.

The dimension of the groove is 1 cm wide and 1 cm deep. The groove will

be symmetric with respect to the heavy spot. How far around the outer

circumference of the impeller should the groove be? Specify the answer

in terms of θ. Hint: Treat the groove as a thin ring of material.

The outer radius of the impeller, at the location of the groove, is 15 cm.

The impeller material is steel, with a density of ρ = 7900 kg/m³.