Rotation 1 Question 6
6. The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of $x$ from it, is ’ $I(x)$ ‘. Which one of the graphs represents the variation of $I(x)$ with $x$ correctly?
(2019 Main, 12 Jan II) (a)
(c)
(b)
(d)
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Answer:
Correct Answer: 6. (b)
Solution:
- Moment of inertia of a solid sphere about an axis through its centre of mass is
$$ I _C=\frac{2}{5} M R^{2} $$
Moment of inertia about a parallel axis at a distance $x$ from axis through its COM is
$I=I _C+M x^{2}$ (by parallel axis theorem)
So graph of I versus $x$ is parabolic are shown
