Rotation 1 Question 15

18. One quarter section is cut from a uniform circular disc of radius $R$. This section has a mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is (2001)

(a) $\frac{1}{2} M R^{2}$

(b) $\frac{1}{4} M R^{2}$

(c) $\frac{1}{8} M R^{2}$

(d) $\sqrt{2} M R^{2}$

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Answer:

Correct Answer: 18. (a)

Solution:

  1. Mass of the whole disc $=4 M$

Moment of inertia of the disc about the given axis

$$ =\frac{1}{2}(4 M) R^{2}=2 M R^{2} $$

$\therefore$ Moment of inertia of quarter section of the disc

$$ =\frac{1}{4}\left(2 M R^{2}\right)=\frac{1}{2} M R^{2} $$



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