Question

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​

Answer 1

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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