(A) The moment of inertia $I$ of a system of point masses about an axis is given by $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of

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(A) The moment of inertia $I$ of a system of point masses about an axis is given by $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of the $i$-th mass from the axis.For the given axis passing through $m_1$ and bisecting the side $m_2m_3$:$1$. The distance of $m_1$ from the axis is $r_1 = 0$.$2$. The distance of $m_2$ from the axis is $r_2 = a/2$.$3$. The distance of $m_3$ from the axis is $r_3 = a/2$.Therefore,the total moment of inertia is:$I = m_1(0)^2 + m_2(a/2)^2 + m_3(a/2)^2$$I = 0 + m_2(a^2/4) + m_3(a^2/4)$$I = (m_2 + m_3) \frac{a^2}{4}$

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

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Three point masses $m_1, m_2, m_3$ are placed at the vertices of an equilateral triangle of side $a$. The moment of inertia of the system about an axis passing through the vertex $m_1$ and perpendicular to the plane of the triangle is not what is asked; rather,the axis passes through $m_1$ and bisects the opposite side $m_2m_3$. What is the moment of inertia of the system about this axis?

A
$ (m_2 + m_3) \frac{a^2}{4} $
B
$ (m_1 + m_2 + m_3) a^2 $
C
$ (m_1 + m_2) \frac{a^2}{4} $
D
$ (m_2 + m_3) a^2 $

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Class 11 Questions

Class 11

Physics Questions

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System of Particles and Rotational Motion

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Moment of Inertia and Radius of gyration

Three particles,each of mass $m$,are placed at the vertices of an equilateral triangle $ABC$ of side length $l$. What is the moment of inertia of the system about the axis $AX$ in the plane of $ABC$,as shown in the figure?

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Four rods are arranged in the form of a square. Calculate the moment of inertia about an axis passing through the center and perpendicular to the plane. (Mass $M$ and length $L$ for each rod)

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Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

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Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$,respectively,about their axes is $I_{1} : I_{2} = 1 : 16$,then the value of $\alpha$ is:

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Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

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Similar Questions

Three particles,each of mass $m$,are placed at the vertices of an equilateral triangle $ABC$ of side length $l$. What is the moment of inertia of the system about the axis $AX$ in the plane of $ABC$,as shown in the figure?

Four rods are arranged in the form of a square. Calculate the moment of inertia about an axis passing through the center and perpendicular to the plane. (Mass $M$ and length $L$ for each rod)

Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$,respectively,about their axes is $I_{1} : I_{2} = 1 : 16$,then the value of $\alpha$ is:

Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

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