when temperature of a rod increases from t to t + delta t , its moment of inertia from l to l+delta l .if alpha 3 is the coefficient of linear expansion of rod ,then delta l/l
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The value of Δl/l = 2αΔT
Explanation:
Moment of inertia of a rod, I = ML212 ….(i)
Where M is the mass and L is the length of the rod.
Δl = 1/12 x 2MLDdL .......(ii)
Dividing equation (ii) by (i)
Δl/l = 2ΔL/L
Since ΔL = LαΔT
= 2( LαΔT)/L
Δl/l = 2αΔT
Thus the value of Δl/l = 2αΔT
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