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

A solid sphere of mass M and radius R having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness I, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

A

`(2R)/(sqrt(15))`

B

`R sqrt((2)/(15))`

C

`(4R)/(sqrt(15))`

D

`(R)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Moment of inertia of solid sphere of mass M and radius R about an axis passing through the centre of mass is `I = (2)/(5) MR^(2)` .
Let the radius of the disc be r .
Moment of inertia of circular disc of radius r and mass M about an axis passing through the centre of mass and perpendicular to its plane `= (1)/(2) Mr^(2)`
Using theorem of parallel axes , moment of inertia of disc about its edge is
`I. = (1)/(2) Mr^(2) + Mr^(2) = (3)/(2) Mr^(2)`
Given `I = I. therefore (2)/(5) MR^(2) = (3)/(2) Mr^(2) or r = (2R)/(sqrt(15))`
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Knowledge Check

  • A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as J, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains J. Then, radius of the disc will be

    A
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    B
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    C
    `(4R)/(sqrt(15))`
    D
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    A
    `(2 R)/(sqrt(15))`
    B
    `R sqrt((2)/(15))`
    C
    `(4 R)/(sqrt(15))`
    D
    `( R)/(4)`

  • A solid sphere of mass M and radius R having tmoment of inertia I about its diameter is recast into a solid dise of radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as

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