One solid sphere A  and another hollow sphere B  are of same mass and same outer radii. Their  moment of inertia about their diameters are respectively I_{A}\: \: and\: \: I_{B}  such that

Option 1)

I_{A }= I_{B}

Option 2)

I_{A }> I_{B}

Option 3)

I_{A }< I_{B}

Option 4)

I_{A }/I_{B}=d_{A }/d_{B}

Where d_{A } and d_{B } are their densities

Answers (1)

As we learnt in

Moment of inertia for solid sphere -

I=\frac{2}{5} MR^{2}

 

- wherein

About a diameter.

 

 Solid sphere I_{s}=\frac{2}{5}MR^{2}

Hollow sphere I_{H}=\frac{2}{3}MR^{2}

\frac{I_{s}}{I_{H}}=\frac{3}{5}    i.e.  I_{s}< I_{H}

I_{s}= I_{A}      

I_{H}= I_{B}  i.e.  I_{H}< I_{B}


Option 1)

I_{A }= I_{B}

This is incorrect option.

Option 2)

I_{A }> I_{B}

This is incorrect option.

Option 3)

I_{A }< I_{B}

This is the correct option.

Option 4)

I_{A }/I_{B}=d_{A }/d_{B}

Where d_{A } and d_{B } are their densities

This is incorrect option.

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