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Q.

A hollow sphere when it is rotating about its own axis at an angular velocity $ω$ has moment of inertia I is partly filled with water. As a result its angular velocity is doubled then its moment of inertia becomes

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An Intiative by Sri Chaitanya

a

Remains same

b

More than I

c

Zero

d

Less than I

answer is A.

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Detailed Solution

We know according to law of conservation of angular momentum

$I_{1} ω_{1} = I_{2} ω_{2}$

$Hollow sphere has I_{1} = I ω_{1} = ω$

$After it is partly filled with water I_{2} = ? ω_{2} = 2 ω$ $Now I ω = I_{2} \times 2 ω$

$∴ I_{2} = I / 2$

So its moment of inertia becomes less than I

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A hollow sphere when it is rotating about its own axis at an angular velocity ωhas moment of inertia I is partly filled with water. As a result its angular velocity is doubled then its moment of inertia becomes