(C) The radius of all bodies is $2R$ and mass is $M$.$I_{1} = \frac{2}{5} M (2R)^{2} = \frac{8}{5} MR^{2}$$I_{2} = \frac{1}{2} M (2R)^{2} = 2 MR^{2}$$

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(C) The radius of all bodies is $2R$ and mass is $M$.$I_{1} = \frac{2}{5} M (2R)^{2} = \frac{8}{5} MR^{2}$$I_{2} = \frac{1}{2} M (2R)^{2} = 2 MR^{2}$$I_{3} = \frac{M (2R)^{2}}{4} = MR^{2}$$I_{4} = \frac{M (2R)^{2}}{2} = 2 MR^{2}$Given equation: $2(I_{2} + I_{3}) + I_{4} = x I_{1}$Substitute the values: $2(2 MR^{2} + MR^{2}) + 2 MR^{2} = x (\frac{8}{5} MR^{2})$$2(3 MR^{2}) + 2 MR^{2} = x (\frac{8}{5} MR^{2})$$6 MR^{2} + 2 MR^{2} = x (\frac{8}{5} MR^{2})$$8 MR^{2} = x (\frac{8}{5} MR^{2})$$x = 5$

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia and Radius of gyration

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Moment of Inertia $(M.I.)$ of four bodies having same mass $M$ and radius $2R$ are as follows:
$I_{1} =$ $M.I.$ of solid sphere about its diameter
$I_{2} =$ $M.I.$ of solid cylinder about its axis
$I_{3} =$ $M.I.$ of solid circular disc about its diameter
$I_{4} =$ $M.I.$ of thin circular ring about its diameter
If $2(I_{2} + I_{3}) + I_{4} = x I_{1}$,then the value of $x$ will be...

JEE MAIN 2022 All JEE MAIN

A
$57$
B
$55$
C
$5$
D
$9$

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Class 11

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System of Particles and Rotational Motion

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Moment of Inertia and Radius of gyration

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$A$ thin rod of total length $4l$ and total mass $4M$ is bent into the shape shown in the figure. Each segment has length $l$ and mass $M$. What is the moment of inertia of the rod about the axis passing through point $O$ and perpendicular to the plane of the paper?

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$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. If their moments of inertia about their diameters are $I_A$ and $I_B$ respectively,then which of the following is true?

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The moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is .......

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$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b, a$) have identical areas and masses. Show that:
$(i) \frac{I_{xR}}{I_{xS}} < 1$
$(ii) \frac{I_{yR}}{I_{yS}} > 1$
$(iii) \frac{I_{zR}}{I_{zS}} > 1$

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The moment of inertia of a solid cylinder of mass $20 \ kg$,length $1 \ m$,and radius $0.2 \ m$ about its geometric axis is (in $kg \cdot m^2$):

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$A$ thin rod of total length $4l$ and total mass $4M$ is bent into the shape shown in the figure. Each segment has length $l$ and mass $M$. What is the moment of inertia of the rod about the axis passing through point $O$ and perpendicular to the plane of the paper?

$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. If their moments of inertia about their diameters are $I_A$ and $I_B$ respectively,then which of the following is true?

The moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is .......

$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b, a$) have identical areas and masses. Show that:$(i) \frac{I_{xR}}{I_{xS}} < 1$$(ii) \frac{I_{yR}}{I_{yS}} > 1$$(iii) \frac{I_{zR}}{I_{zS}} > 1$

The moment of inertia of a solid cylinder of mass $20 \ kg$,length $1 \ m$,and radius $0.2 \ m$ about its geometric axis is (in $kg \cdot m^2$):

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$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b, a$) have identical areas and masses. Show that:
$(i) \frac{I_{xR}}{I_{xS}} < 1$
$(ii) \frac{I_{yR}}{I_{yS}} > 1$
$(iii) \frac{I_{zR}}{I_{zS}} > 1$