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Find the moment of inertia of a uniform ...

Find the moment of inertia of a uniform cylinder about an axis through its centre of mass and perpendicular to its base. Mass of the cylinder is M and radius is R.

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To find the moment of inertia of a uniform cylinder about an axis through its center of mass and perpendicular to its base, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Geometry**: - We have a uniform cylinder with mass \( M \) and radius \( R \). The axis of rotation is through its center and perpendicular to its base. 2. **Use the Definition of Moment of Inertia**: ...
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State the expression for the moment of inertia of a thin uniform rod anout an axis through its centre of mass and perpendicular to its length. Hence deduce the expression for its moment of inertia about an axis through its one end and perpendicular to its length.

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Knowledge Check

  • The moment of inertia of a uniform semi - circular disc about an axis passing through its centre of mass and perpendicular to its plane is ( Mass of this disc is M and radius is R ) .

    A
    `(MR^2)/2-M((2R)/pi)^2`
    B
    `(MR^2)/2-M((4R)/pi)^2`
    C
    `(MR^2)/2+M((4R)/(3pi))^2`
    D
    `(MR^2)/2+M((2R)/(pi))^2`

  • Moment of inertia of a uniform quarter disc of radius R and mass M about an axis through its centre of mass and perpendicular to its plane is :

    A
    `(MR^(2))/(2)-M((4R)/(3pi))^(2)`
    B
    `(MR^(2))/(2)-M(sqrt(2)(4R)/(3pi))^(2)`
    C
    `(MR^(2))/(2)+M((4R)/(3pi))^(2)`
    D
    `(MR^(2))/(2)+M(sqrt(2)(4R)/(3pi))^(2)`

  • The radius of gyration of an uniform rod of length L about an axis passing through its centre of mass and perpendicular to its length is.

    A
    `(L)/(sqrt(2))`
    B
    `(L^2)/(sqrt(12))`
    C
    `(L)/(sqrt(3))`
    D
    `(L)/(sqrt(2))`

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    The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its centre of mass and perpendicular to its plane is mr^(2)(-(k)/(pi^(2))) . Find the value of k.

    The moment of inertia of a square plate of mass 4kg and side 1m about an axis passing through its centre and perpendicular to its plane is

    The moment of inertia of a uniform semicircular wire of mass M and radius R about an axis passing through its centre of mass and perpendicular to its plane is x(MR^(2))/(10) . Find the value of x ? (Take pi^(2)=10 )

    The moment of inertia of a solid cylinder of mass M, length 2R and radius R about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is I_(1) and about an axis passing through one end of the cylinder and perpendicular to the axis of cylinder is I_(2)

    The moment of inertia of a solid cylinder of mass M, length 2 R and radius R about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is I, and about an axis passing through one end of the cylinder and perpendicular to the axis of cylinder is I_2 then

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