To solve this problem, we need to calculate the correct diameter of the steel ball using the screw gauge readings.$\\$Given:$\\$• Least count of the screw gauge $= 0.001$ cm$\\$• Main scale reading $= 5$ mm$= 0.5$ cm$\\$• Circular scale reading $= 25$ divisions$\\$• Zero error $= -0.004$ cm$\\$First, calculate the circular scale contribution to the measurement:$\\$Circular scale reading in cm$= 25 \times 0.001 = 0.025$ cm$\\$Now, calculate the total reading without considering zero error:$\\$Total reading$=$Main scale reading$+$Circular scale reading$\\$Total reading$= 0.5 + 0.025 = 0.525$ cm$\\$Apply the zero error correction:$\\$Corrected diameter$=$Total reading$-$Zero error$\\$Corrected diameter$= 0.525 - (-0.004) \\$Corrected diameter$= 0.525 + 0.004 = 0.529$ cm$\\$Therefore, the correct diameter of the ball is $0.529$ cm, which corresponds to Option 4.