The moment of inertia of a uniform circular disc (figure) is maximum about an axis perpendicular to the disc and passing through
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The distribution of mass about axis is minimum so radius of gyration is minimum and therefore moment of inertia is minimum about .
Three particles, each of mass gram, are situated at the vertices of an equilateral triangle of side (as shown in the figure). The moment of inertia of the system about a line perpendicular to and in the plane of , in gram- units will be
A raw egg behaves like a spherical shell and a half boiled egg behaves like a solid sphere
The moment of inertia of the rectangular plate is minimum along the axis
A C
In a hollow sphere, the mass is distributed away from the axis of rotation. So, its moment of inertia is greater than that of a solid sphere.
Of the two eggs which have identical sizes, shapes and weights, one is raw, and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is
one
less than one
greater than one
not comparable
One solid sphere and another hollow sphere are of same mass and same outer radii, Their moments of inertia about their diameters are respectively and , such that
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
The moment of inertia of a thin uniform rod of mass and length about an axis passing through its midpoint and perpendicular to its length is . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
By theorem of parallel axes,
each of value , are placed at the corners of a square of side . The moment of inertia of this system about an axis passing through and parallel to is
M.I due to the point mass at M.I due to the point mass at M.I due to the point mass at .
Consider a uniform square plate of side ' ' and mass ' '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Point masses and are lying at the points , and respectively. The moment of inertia of this system about -axis will be
Moment of inertia of the whole system about the axis of rotation will be equal to the sum of the moments of inertia of all the particles.
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