One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is [2001]

Question

Smart Achievers · Accepted Answer

(1)

$Mass of disc = 4 M$

$I_{disc} = \frac{1}{2} M R^{2}$

$∴$ $Moment of inertia of one quarter of disc$

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

Solution

Q.
One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is [2001]

1 $\frac{1}{2} M R^{2}$

2 $\frac{1}{4} M R^{2}$

3 $\frac{1}{8} M R^{2}$

4 $\sqrt{2} M R^{2}$

Ans.
(1)

$Mass of disc = 4 M$

$I_{disc} = \frac{1}{2} M R^{2}$

$∴$ $Moment of inertia of one quarter of disc$

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

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Solution

Q. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is [2001]

1 12MR2

2 14MR2

3 18MR2

4 2MR2

Ans. (1) Mass of disc=4M Idisc=12MR2 ∴ Moment of inertia of one quarter of disc =14[12(4M)R2]=12MR2