question_answer

The moment of inertia of a solid sphere about a tangent is \[\frac{5}{3}M{{R}^{2}}\], where M is mass and R is radius of the sphere. Find the M.I. of the sphere about its diameter.

Answer:

                Here      \[{{I}_{T}}=\frac{5}{3}M{{R}^{2}}\] Now diameter of sphere is an axis passing through its centre of mass. By using theorem of parallel axes, \[{{I}_{T}}={{I}_{CM}}+M{{R}^{2}}\]                 \[\therefore \]  \[{{I}_{CM}}={{I}_{T}}-M{{R}^{2}}=\frac{5}{3}M{{R}^{2}}\]           \[-M{{R}^{2}}=\frac{2}{3}M{{R}^{{}}}\]