Rotational Motion Question 10
Question: One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $ I _{A} $ and $ I _{B} $ such that where $ d _{A} $ and $ d _{B} $ are their densities.
[AIEEE 2004]
Options:
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}} $
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Answer:
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}MR^{2} $ …(i)
Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter $ l _{B}=\frac{2}{3}MR^{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=mr^{2} $ .
So, hollow sphere has large $ l $ , because it has mass only on its circumference.
