(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

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$57$
B
$55$
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$5$
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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Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively,and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $\frac{r_2}{r_1}$ equals:

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$A$ system consists of two identical spheres,each of mass $1.5\, {kg}$ and radius $50\, {cm}$,attached to the ends of a light rod. The distance between the centers of the two spheres is $5\, {m}$. What is the moment of inertia of the system about an axis perpendicular to the rod and passing through its midpoint? (in ${kgm}^{2}$)

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The moment of inertia of a body depends on

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Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?

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Three point masses $m_1, m_2$,and $m_3$ are placed at the vertices of an equilateral triangle of side $a$. Find the moment of inertia of this system about the altitude passing through $m_1$.

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Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively,and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $\frac{r_2}{r_1}$ equals:

The moment of inertia of a body depends on

Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?

Three point masses $m_1, m_2$,and $m_3$ are placed at the vertices of an equilateral triangle of side $a$. Find the moment of inertia of this system about the altitude passing through $m_1$.

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