91Ó°ÊÓ

A sinusoidal voltage \(v=100 \sin \omega t\) volts. Use integration to determine over half a cycle (a) the mean value, and (b) the rms value.

Determine the co-ordinates of the centroid of the area lying between the curve \(y=5 x-x^{2}\) and the \(x\)-axis.

A metal disc has a radius of \(5.0 \mathrm{~cm}\) and is of thickness \(2.0 \mathrm{~cm}\). A semicircular groove of diameter \(2.0 \mathrm{~cm}\) is machined centrally around the rim to form a pulley. Determine, using Pappus' theorem, the volume and mass of metal removed and the volume and mass of the pulley if the density of the metal is \(8000 \mathrm{~kg} \mathrm{~m}^{-3}\)