Two small spheres are connected by a very light rigid rod along the –axis

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

Problem

Two small spheres are connected by a very light rigid rod along the

x

–axis. Sphere 1 has mass

0.30\,\text{kg}

and is located at

x=0

. Sphere 2 has mass

0.20\,\text{kg}

and is fixed at

x=0.40\,\text{m}

. An experimental apparatus will rotate the assembly about an axis that is perpendicular to the

xy

–plane and parallel to the

z

–axis, passing through a point on the

x

–axis located a distance

d

from the system’s center of mass. For safety, the rotational inertia of the assembly about that axis must not exceed

0.050\,\text{kg}\cdot\text{m}^2

. (a) Determine the

x

–coordinate of the center of mass of the two–sphere system. (b) Derive an expression for the rotational inertia

I(d)

of the system about the described axis in terms of

d

. (c) Calculate the maximum magnitude of

d

that keeps

I(d)

less than or equal to

0.050\,\text{kg}\cdot\text{m}^2

. Provide your answer with units. (d) Discuss whether the allowable axis locations lie between the two spheres, outside both spheres, or in some other region, and justify your answer based on the numerical result from part (c).

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