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A solid sphere of mass M and radius R ha...

A solid sphere of mass M and radius R has a moment of inertia about an axis tangent to its surface is given by formula …………..

A

`(2)/(5)MR^(2)`

B

`(7)/(5)MR^(2)`

C

`(2)/(3)MR^(2)`

D

`(5)/(3)MR^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Moment of inertia of solid sphere about an axis passing through its centre `I_(c )=(2)/(5)MR^(2)`
From parallel axis theorem, moment of inertia about axis tangential to surface,
`I=I_(c)+Md^(2)`
`=(2)/(5)MR^(2)+MR^(2) [because d=R]`
`therefore I=(7)/(5)MR^(2)`
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Knowledge Check

  • The ratio of moment of inertia about axis of a ring to a axis of disc of same mass and radius is …………….

    A
    `1:1`
    B
    `2:1`
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  • Two identical concentric rings each of mass (m) and radius (r ) placed perpendicularly. So the moment of inertia about axis of one of the ring is …………..

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    `(1)/(2)mr^(2)`
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    `mr^(2)`
    C
    `(3)/(2)mr^(2)`
    D
    `2mr^(2)`

  • A solid sphere of mass m and radius R rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ((E_("sphere"))/(E_("cylinder"))) will be = ..............

    A
    `1:4`
    B
    `3:1`
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    `2:3`
    D
    `1:5`

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