question_answer

A circular disc X of radius R is made from an iron plate of thickness t, and another plate Y of radius 4R is made from an iron plate of thickness t/ 4. The ratio of moments of inertia \[{{I}_{Y}}/{{I}_{X}}\]is

A)  32                                         

B)  16

C)  1                                            

D)   64

Correct Answer: D

Solution :

                  The moment of inertia of\[X\]                 \[{{I}_{X}}=\frac{1}{2}{{M}_{X}}{{R}^{2}}\] Mass of\[X\]plate\[=volume\times density\]                 \[{{M}_{X}}=(\pi {{R}^{2}}t)\rho \] \[\therefore \]  \[{{I}_{X}}=\frac{1}{2}(\pi {{R}^{2}}t)\rho {{R}^{2}}\] The moment of inertia of Y                 \[{{I}_{Y}}=\frac{1}{2}{{M}_{y}}(4{{R}^{2}})\] Mass of\[y\]plate \[=volume\times density\]                 \[{{M}_{Y}}=(\pi {{(4R)}^{2}}t)\rho \] \[\therefore \]  \[{{I}_{Y}}=\frac{1}{2}(\pi 16{{R}^{2}}\frac{t}{4}\rho )16{{R}^{2}}\] The ratio of moments of inertia                                 \[\frac{{{I}_{Y}}}{{{I}_{X}}}=64\]