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Chapter 8: Problem 8

The center of mass of an irregular rigid object is always located a) at the geometrical center of c) both of the above the object. d) none of the above b) somewhere within the object.

Short Answer

Expert verified
Answer: The center of mass of an irregular rigid object is always located somewhere within the object.

Step by step solution

01

Define center of mass

The center of mass is a point within or near an object where the object's mass is considered to be concentrated. In general, the center of mass can be located by the average position of all particles that make up the object.
02

Evaluate option a)

In option a), it's proposed that the center of mass is always located at the geometrical center of the object. This may be true for symmetric objects with uniform mass distribution, but for irregular objects, the mass may be unevenly distributed. In such cases, the center of mass will not be at the geometrical center. So, option a) is not correct.
03

Evaluate option b)

In option b), it's proposed that the center of mass is always located somewhere within the object. This is a more general statement, as it accounts for both regular and irregular rigid objects. For irregular objects with uneven mass distribution, their center of mass may not be at the geometrical center but still located within the object. This option seems correct.
04

Evaluate option c)

Option c) suggests that both options a) and b) are correct. However, we have already evaluated both options and determined that option a) is not always correct. Therefore, option c) cannot be correct.
05

Evaluate option d)

Option d) states that none of the above options are correct. Since we have found that option b) is correct, option d) is not correct. #Conclusion#From our analysis of each option, we found that option b) is the correct one. The center of mass of an irregular rigid object is always located somewhere within the object.

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Most popular questions from this chapter

A cart running on frictionless air tracks is propelled by a stream of water expelled by a gas-powered pressure washer stationed on the cart. There is a \(1.00-\mathrm{m}^{3}\) water tank on the cart to provide the water for the pressure washer. The mass of the cart, including the operator riding it, the pressure washer with its fuel, and the empty water tank, is \(400 . \mathrm{kg} .\) The water can be directed, by switching a valve, either backward or forward. In both directions, the pressure washer ejects \(200 .\) L of water per min with a muzzle velocity of \(25.0 \mathrm{~m} / \mathrm{s}\). a) If the cart starts from rest, after what time should the valve be switched from backward (forward thrust) to forward (backward thrust) for the cart to end up at rest? b) What is the mass of the cart at that time, and what is its velocity? (Hint: It is safe to neglect the decrease in mass due to the gas consumption of the gas-powered pressure washer!) c) What is the thrust of this "rocket"? d) What is the acceleration of the cart immediately before the valve is switched?

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