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The moment of inertia of a solid cylinde...

The moment of inertia of a solid cylinder of mass M, length 2 R and radius about R 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

A

`l_(1)ltl_(2)`

B

`l_(2)-l_(1)=MR^(2)`

C

`(l_(2))/(l_(1))=(19)/(12)`

D

`(l_(2))/(l_(1))=(7)/(6)`

Text Solution

Verified by Experts

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 is
`I_(1)=M(L^(2)/(12)+(R^(2))/(4))`
`I_(2)=M[(4R^(2))/(12)+(R^(2))/(4)]=M[(7R^(2))/(12)]`
Moment of inertia passing through one end of the cylinder and perpendicular to the axis of the cylinder
`=M[(19R^(2))/(12)]`
`I_(2)-I_(1)=MR^(2)`
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Knowledge Check

  • Moment of inertial of a uniform horizontal solid cylinder of mass M about an axis passing through its edge and perpendicular to the axis of the cylinder when its length is 6 times its radius R is

    A
    `(39MR^(2))/(4)`
    B
    `(30MR^(2))/(4)`
    C
    `(49MR)/(4)`
    D
    `(49MR^(2))/(4)`

  • M.I of a uniform horizontal solid cylinder of mass M about an axis passing through its edge and perpendicular to the axis of cylinder when its length is 6 times of its radius R is

    A
    `(39)/(4)MR^(2)`
    B
    `(39)/(2)MR^(2)`
    C
    `(49)/(4)MR^(2)`
    D
    `(49)/(2)MR^(2)`

  • M.I of a uniform horizontal solid cylinder of mass M about an axis passing through its edge and perpendicular to the axis of cylinder when its length is 6 times of its radius R is

    A
    `(39)/(4)MR^(2)`
    B
    `(39)/(2)MR^(2)`
    C
    `(49)/(4)MR^(2)`
    D
    `(49)/(2)MR^(2)`

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