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Heat and Temperature — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsHeat and Temperature1 Mark
MCQ
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia Iabout a line parallel to itself will increase by:
  • A
    $\text{Zero}$
  • B
    $\alpha\text{I}\Delta\text{t}$
  • ✓
    $2\alpha\text{I}\Delta\text{t}$
  • D
    $3\alpha\text{I}\Delta\text{t}$
✓

Answer

Correct option: C.
$2\alpha\text{I}\Delta\text{t}$
The moment of inertia of a solid body of any shape changes with temperature as
$\text{I}'=\text{I}(1+2\alpha\Delta\text{t})$
Here, I = initial moment of inertia
I' = new moment of inertia due to change in temperature
$\alpha=\text{expansion coefficient}$
$\Delta\text{t}=\text{change in temperature}$
$\text{So},\text{I}'-\text{I}=2\alpha\text{I}\Delta\text{t}$

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