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From a solid sphere of M and radius R a ...

From a solid sphere of M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendiular to one of its faces is:

A

`(4MR^(2))/(9sqrt(3pi))`

B

`(4MR^(2))/(3sqrt(3pi))`

C

`(MR^(2))/(32sqrt(2pi))`

D

`(MR^(2))/(16sqrt(2pi))`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is : (4MR^(2))/(3sqrt(3)pi)

    A
    `(4MR^(2))/(3sqrt(3)pi)`
    B
    `(MR^(2))/(32sqrt(2)pi)`
    C
    `(MR^(2))/(16sqrt(2)pi)`
    D
    `(4MR^(2))/(9sqrt(3)pi)`

  • The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

    A
    increases if its temperature is increased
    B
    changes if its axis of rotation is changed
    C
    increases if its angular velocity is increased
    D
    both (a) and (b) are correct

  • The moment of inertia of a sphere of radius R about an axis passing through its centre is proportional to-

    A
    `R^2`
    B
    `R^3`
    C
    `R^4`
    D
    `R^5`
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