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