question_answer 58)

                  A uniform square plate S (side c) and a uniform rectangular plate R (sides b, a) have identical areas and masses.                 Show that (i) \[{{I}_{xR}}/{{I}_{xS}}\,<\,1;\]                       (ii) \[{{I}_{yR}}/{{I}_{yS}}>1;\] (iii) \[{{I}_{zR}}/{{I}_{zS}}>1\].                

Answer:

                  Area of rectangular plate = Area of square plate i.e. \[ab={{c}^{2}}\]                 Now \[{{I}_{xR}}\,=\,\frac{m{{b}^{2}}}{12}\] and \[{{I}_{xS}}\,=\frac{m{{c}^{2}}}{6}\]