(A) The moment of inertia of a disc about an axis passing through its center of mass and perpendicular to its plane is given by $I_{cm} = \frac{1}{2}

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(A) The moment of inertia of a disc about an axis passing through its center of mass and perpendicular to its plane is given by $I_{cm} = \frac{1}{2} MR^2$. Given $M = 1 \,kg$ and $R = 2 \,m$,$I_{cm} = \frac{1}{2} \times 1 \times (2)^2 = 2 \,kg \cdot m^2$. According to the parallel axis theorem,the moment of inertia about an axis parallel to the $XY$ axis and passing through the edge of the disc is $I' = I_{cm} + Md^2$,where $d = R$ is the distance between the two axes. Substituting the values,$I' = 2 + (1 \times 2^2) = 2 + 4 = 6 \,kg \cdot m^2$.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia of Compound Bodies and Theorem of Moment of Inertia

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The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis $XY$ passing through its center of mass and perpendicular to the plane of the disc is $2 \,kg \,m^2$. The moment of inertia about an axis parallel to the axis $XY$ and passing through the edge of the disc is

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A
$6 \,kg \,m^2$
B
$4 \,kg \,m^2$
C
$10 \,kg \,m^2$
D
$8 \,kg \,m^2$

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System of Particles and Rotational Motion

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Moment of Inertia of Compound Bodies and Theorem of Moment of Inertia

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The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis $XY$ passing through its center of mass and perpendicular to the plane of the disc is $2 \,kg \,m^2$. The moment of inertia about an axis parallel to the axis $XY$ and passing through the edge of the disc is

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Four identical solid spheres each of mass $m$ and radius $a$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about one side of the square is:

$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

For a uniform rectangular sheet shown in the figure,the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $O$ (the centre of mass) and $O'$ (corner point) is

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