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A metallic solid sphere is rotating about its diameter as axis of rotation . If the temperature is increased by 200∘C200∘C, the percentage increase in its moment of inertia is : (Coefficient of linear expansion of the metal =10−5/∘C=10−5/∘C)
Asked by Atulcaald | 31 May, 2018, 09:30: PM
Change in volume δV due to thermal expansion is given by

where V0 is initial volume, γ is volume expansion coefficient and ΔT is increase of temperature.

change in volume as a function of change in radius is given by

from (1) and (2), we get
where α is linear expansion coefficient ( γ = 3α )

Moment of inertia I is given by, I = K×R2 ....................(4)
where all constants are clubbed together as K.

change in moment of inertia δI due to change in radius δR is given by,
δI = 2×R×K×δR ...................(5)

from (4) and (5), we get ...................(6)
using eqn(3), we rewrite eqn(6) to get percentage change as,
Answered by Thiyagarajan K | 09 Jun, 2018, 11:09: AM

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