PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Two identical metal spheres, each of mass 0.25kg, are rigidly connected by a very light rod of length 0.50m. The assembly is free to rotate in a horizontal plane about a vertical axle that intersects the rod at a point 0.10m from the right-hand sphere, as shown in the verbal description below.
Verbal diagram description (not drawn to scale):
• Rod lies horizontally; right sphere labelled A, left sphere labelled B.
• A vertical axle pierces the rod between the spheres, closer to A; the distance from the axle to A is 0.10m.
When the assembly is set rotating about the axle, its rotational inertia is measured to be 0.042kg⋅m2.
(a) Determine the distance between the axle and the center of mass of the sphere–rod system. Show your reasoning clearly.
(b) Using the measured rotational inertia, calculate the rotational inertia of the assembly about an axle through its center of mass and perpendicular to the rod.
(c) Compare your result from part (b) with the value that would be obtained by treating each sphere as a point mass located at its center. Discuss whether the light rod’s mass can be considered negligible in this experiment and how you can tell.