A) \[{{I}_{A}}={{I}_{B}}\]
B) \[{{I}_{A}}>{{I}_{B}}\]
C) \[{{I}_{A}}<{{I}_{B}}\]
D) \[\frac{{{I}_{A}}}{{{I}_{B}}}<\frac{{{d}_{A}}}{{{d}_{B}}}\]
Correct Answer: C
Solution :
| [c] Let same mass and same outer radii of solid sphere and hollow sphere are M and R, respectively. |
| The moment of inertia of solid sphere A about its diameter |
| \[{{l}_{A}}=\frac{2}{5}\,M{{R}^{2}}\] ...(i) |
| Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter |
| \[{{l}_{B}}=\frac{2}{3}\,M{{R}^{2}}\] ...(ii) |
| It is clear from Eqs. (i) and (ii), \[{{l}_{A}}<{{l}_{B}}\]. |
| Alternatively |
| We can say that the object which has mass at greater distance will have higher moment of inertia as \[l=m{{r}^{2}}\]. So, hollow sphere has large\[l\], because it has mass only on its circumference. |
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