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Chapter 8: 8-6MCQ (page 198)

Two spheres have the same radius and equal mass. One sphere is solid, and the other is hollow and made of a denser material. Which one has the bigger moment of inertia about an axis through its center?

(a) The solid one.

(b) The hollow one.

(c) Both the same.

Short Answer

Expert verified

The correct option is (b).

Step by step solution

01

Magnitude of inertia

The moment of inertia of a body is the product of the mass and the square of the distance from the axis of rotation.Now, the moment of inertia increases when the mass is at a larger distance from the axis of rotation.

The mass and radius of both solid and hollow spheres are the same.

02

Explanation

For a solid sphere, the mass is distributed over the whole spherical region.

However, for the other hollow sphere, the mass is only at the surface of the spherical region.

Both have the same radius and mass, and the mass for the hollow sphere is at a larger distance than the solid sphere from the rotational axis.

Hence, the moment of inertia is more for the hollow sphere.

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Most popular questions from this chapter

A merry-go-round with a moment of inertia equal to \({\bf{1260}}\;{\bf{kg}} \cdot {{\bf{m}}{\bf{2}}}\) and a radius of 2.5 m rotates with negligible friction at \({\bf{1}}{\bf{.70}}\;{{{\bf{rad}}} \mathord{\left/ {\vphantom {{{\bf{rad}}} {\bf{s}}}} \right. \\{\bf{s}}}\). A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to \({\bf{1}}{\bf{.35}}\;{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.

\\{\bf{s}}}\). What is her mass?

The bolts on the cylinder head of an engine require tightening to a torque of 95 m N. If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end? If the six-sided bolt head is 15 mm across (Fig. 8–44), estimate the force applied near each of the six points by a wrench.

Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim and tire have a combined mass of 1.1 kg. The mass of the hub (at the center) can be ignored (why?).

Can a small force ever exert a greater torque than a larger force? Explain.

A uniform rod of mass M and length l can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–63. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–20g.]
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