(D) Let the mass of each sphere be $m = 5 \ kg$ and the length of the rod be $L = 1 \ m$.Case $1$: Axis passing through $A$ and perpendicular to the r

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(D) Let the mass of each sphere be $m = 5 \ kg$ and the length of the rod be $L = 1 \ m$.Case $1$: Axis passing through $A$ and perpendicular to the rod.The moment of inertia $I_1$ is given by:$I_1 = m_A \cdot (0)^2 + m_B \cdot (L)^2 = 0 + m \cdot (1)^2 = m$Case $2$: Axis passing through the center of the rod and perpendicular to it.The moment of inertia $I_2$ is given by:$I_2 = m_A \cdot (L/2)^2 + m_B \cdot (L/2)^2 = m \cdot (0.5)^2 + m \cdot (0.5)^2 = 0.25m + 0.25m = 0.5m = m/2$Ratio of moments of inertia:$I_1 / I_2 = m / (m/2) = 2 / 1$Thus,the ratio is $2 : 1$.

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

Medium

Two spheres $A$ and $B$,each of mass $5 \ kg$,are attached to the ends of a light rod of length $1 \ m$. Treating the spheres as point masses,find the ratio of the moment of inertia of the system about an axis passing through $A$ to that about an axis passing through the center of the rod,both axes being perpendicular to the rod.

A
$1 : 1$
B
$1 : 4$
C
$1 : 2$
D
$2 : 1$

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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

The moment of inertia of an object is effective during:

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$A$ rigid body can be hinged about any point on the $x$-axis. When it is hinged such that the hinge is at $x$,the moment of inertia is given by $I = 2x^2 - 12x + 27$. The $x$-coordinate of the centre of mass is:

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Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

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Three point masses $m$ are placed at the corners of an equilateral triangle of side length $\ell$. What is the moment of inertia of the system about an axis passing through one side of the triangle?

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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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The moment of inertia of an object is effective during:

$A$ rigid body can be hinged about any point on the $x$-axis. When it is hinged such that the hinge is at $x$,the moment of inertia is given by $I = 2x^2 - 12x + 27$. The $x$-coordinate of the centre of mass is:

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

Three point masses $m$ are placed at the corners of an equilateral triangle of side length $\ell$. What is the moment of inertia of the system about an axis passing through one side of the triangle?

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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