When the temperature of a uniform rod is slightly raised by t , its moment of inertia I about an axis parallel to itself increases by

Step-by-step solution

The moment of inertia of a body about any axis is given by I = r^2 dm , where r is the perpendicular distance of the mass element dm from the axis of rotation. When the temperature is raised by t , the linear dimensions of the rod increase due to thermal expansion. The new perpendicular distance of each mass element from the axis becomes: r' = r(1 + t) where is the coefficient of linear expansion. The new moment of inertia is: I' = (r')^2 dm = r^2 (1 + t)^2 dm Since is very small, we can neglect the higher-order te