2. The moment of inertia of a thin rod of mass M and length L about an axis pass

Question

2. The moment of inertia of a thin rod of mass M and length L about an axis passing through its centre and normal to its length is given by ML2 /12. Using theorem of parallel axes, find its moment of inertia about an axis passing through on end and normal to its length, if L = 1m and M = 0.2 Kg.

3. Define thermal conductivity of a material. What is its SI Unit? A cubical thermocol box, full of ice, has side 50cm and thickness of 4.0 cm. If outside temperature is 400C, find the amount of ice melted in five hours when the thermal conductivity of thermocol is 0.01 Js–1m–1oC and latent heat of fusion of ice is 335 Jg–1

Explanation / Answer

Parallel-axis Theorem

For an object of mass M, the parallel-axis theorem states:

I = Icom + Mh2

where h is the distance from the center-of-mass to the current axis of rotation, and Icom is the moment of inertia for the object rotating about the axis through the center of mass that is parallel to the current axis.

I = ML^2 / 12 + M(L/2)^2 = ML^2 / 3

A measure of the ability of a material to allow the flow of heat from its warmer surface through the material to its colder surface, determined as the heat energy transferred per unit of time and per unit of surface area divided by the temperature gradient, which is the temperature difference divided by the distance

In SI units, thermal conductivity is measured in watts per meter kelvin (W/(m·K)).

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