A uniform cylinder of steel of mass M, radius R is placed on frictionless bearings and set to rotate about its vertical axis with angular velocity ω0.After the cylinder has reached the specified state of rotation it is heated without any mechanical contact from temperature T0 to T0+ΔT.If ΔI/I is the fractional change in moment of inertia of the cylinder and Δω/ω be the fractional change in the angular velocity of the cylinder and α be the coefficient of linear expansion then
(A) ΔI/I=2ΔR/R
(B) ΔI/I= -Δω/ω0
(C) Δω/ω0= -2αΔT
(D) ΔI/I= -2Δ/R
481Anirban is d answer A.B and C?
Anurag Ghosh Haan it should be A,B and C.......can't get wat D option is..
I=MR^2/2,dI=M*R*dR........dI/I=2*dR/R(1) ........Now Iω0=constant....After partially differentiating,we get dI/I=-dω/ω0(2)......Now,dR=RαΔT(3),now putting (3) in (1) and solving wid (2) we get dω/ω0= -2αΔT(4)
So,A,B and C are correct options.....