SATHEE: Rotation 1 Question 6

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

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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?

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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?