A planar assembly is constructed from three small spheres that may be treated as…

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A planar assembly is constructed from three small spheres that may be treated as point masses. Their positions in the

xy

-plane and their masses are listed below. • Sphere A: mass

0.40\,\text{kg}

located at

x=0\,\text{m},\;y=0\,\text{m}

• Sphere B: mass

0.40\,\text{kg}

located at

x=0.30\,\text{m},\;y=0\,\text{m}

• Sphere C: mass

0.60\,\text{kg}

located at

x=0\,\text{m},\;y=0.40\,\text{m}

Two candidate rotation axes are being considered, each perpendicular to the

xy

-plane: • Axis P passes through the center of mass of the assembly. • Axis Q passes through Sphere A. Answer all parts (a)–(d). (a) Determine the coordinates of the center of mass of the three-sphere assembly. (b) Calculate the rotational inertia of the assembly about Axis P. (c) Calculate the rotational inertia of the assembly about Axis Q. (d) Identify which axis, P or Q, yields the smaller rotational inertia and briefly justify your choice based on the numerical results obtained.

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