question_answer 44)

                  With reference to Fig. of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.) (a) The moment of inertia of cube about z-axis is \[{{I}_{z}}={{I}_{x}}+\,{{I}_{y}}\] (b) The moment of inertia of cube about z? is \[I{{'}_{z}}={{I}_{z}}+\frac{m{{a}^{2}}}{2}\] (c) The moment of inertia of cube about z? is \[={{I}_{z}}=\frac{m{{a}^{2}}}{z}\] (d) \[{{I}_{x}}={{I}_{y}}\]                

Answer:

                  (b, d) \[{{I}_{Z}}={{I}_{x}}+{{I}_{y}}\] is true only for a lamina.