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A unifom cylinder of steel of mass M radius R is placed on frictionless bearings and sct to rotate about its axis with angular velocity `omega_(0)` After the cylinder has reached the specified state of rotation, it is heated from temperature `T_(0)to (T_(0)+DeltaT)` without any mechanical contact. If (DeltaI)/I is the fractional change in moment of inertia of the cylinder and `(Deltaomega)/(omega_(0))` be the fractional change in the angular velocity of the cylinder and alpha be the coefficient of linear expansion, thenA. `(DeltaI)/I=(2DeltaR)/R`B. `(DeltaI)/I=(2Deltaomega)/(omega_(0))`C. `(Deltaomega)/(omega_(0))=-2alphaDeltaT`D. `(DeltaI)/I=-(2DeltaR)/R` |
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Answer» Correct Answer - A::C `I=(MR^(2))/2` &Mis constantRightarrow`IalphaR^(2)` `:.(DeltaI)/I=2((DeltaR)/R)=2alpha(DeltaT)` on heating also no external torque present :.`L=Iw`=constant `:.w alpha1/I` `:.(Deltaw)/w=-(DeltaI)/I=-((DeltaR)/R)=-2alpha(DeltaT)` |
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