Three small lead spheres, each of mass 0.20kg, are kept fixed on a thin light rod along a straight line. A vertical axis AA′ passes through the rod at the 20cm mark of a metre scale placed along the rod.
Spheres P, Q and R are attached at the 0cm, 40cm and 90cm marks respectively.
Answer the following questions in the order given.
(i) Define moment of inertia for a system of discrete particles about a given axis.
(ii) Write, without performing any numerical substitution, the symbolic expression for the moment of inertia of the above system about the axis AA′.
(iii) Explain qualitatively, without calculation, how the moment of inertia will change if the sphere at the 90cm mark is shifted to the 70cm mark, the other spheres remaining fixed.
(iv) Give one reason why the mass of the supporting rod can be neglected in this calculation.