(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

Difficult

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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System of Particles and Rotational Motion

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Moment of Inertia and Radius of gyration

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

DifficultAIPMT 2004

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$A$ circular disc of radius $b$ has a hole of radius $a$ at its centre (see figure). If the mass per unit area of the disc varies as $\sigma(r) = \frac{\sigma_0}{r}$,then the radius of gyration of the disc about its axis passing through the centre is

DifficultJEE MAIN 2019

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The moment of inertia of a thin uniform rod about a perpendicular axis passing through one of its ends is $I$. Now,the rod is bent into a ring and its moment of inertia about its diameter is $I_{1}$. Then $\frac{I}{I_{1}}$ is:

EasyMHT CET 2020

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If the diameter of a flywheel is increased by $1\%$,then the percentage increase in its moment of inertia about an axis passing through its center will be ....... $\%$

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$A$ thin wire of length $l$ and mass $m$ is bent in the form of a semicircle. The moment of inertia about an axis perpendicular to its plane and passing through the end of the wire is .............

Medium

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The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

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