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Chapter 5: Problem 555

Identify the correct statement for the rotational motion of a rigid body \(\\{A\\}\) Individual particles of the body do not undergo accelerated motion \\{B \\} The centre of mass of the body remains unchanged. \\{C\\} The centre of mass of the body moves uniformly in a circular path \\{D\\} Individual particle and centre of mass of the body undergo an accelerated motion.

Short Answer

Expert verified
The correct statement for the rotational motion of a rigid body is \(D: \textrm{Individual particle and centre of mass of the body undergo an accelerated motion}\).

Step by step solution

01

Identify the Key Concepts

The first step to solve this exercise is to recall the basics of rotational motion of a rigid body. A rigid body is an object with a shape that does not change. In rotational motion, every particle of the body moves in a circular path about a line. This line, also called the axis of rotation, penetrates the body. Contrary to translational motion, particles in a rigid body do not all have the same velocity or acceleration.
02

Evaluate Statement A

For a rigid body in rotational motion, all particles move about the axis in circular paths. This means that these particles are undergoing an accelerated motion, given the constant change of the motion direction. Remember that acceleration is defined as any change in the velocity of an object, which includes both magnitude and direction changes. Therefore, statement A is incorrect.
03

Evaluate Statement B

The center of mass of a rigid body in rotation does not necessarily remain unchanged. It depends on the type of rotation. In cases of pure rotation, the center of mass is fixed, but in cases of rolling or general plane motion, for example, the center of mass can change its position over time. Therefore, statement B can be true in some circumstances, but not in all. It is a partially correct statement.
04

Evaluate Statement C

Regarding statement C, It is also not a universally true statement. The center of mass of a rotating body does not always move uniformly in a circular path. As before, this depends on the specific type of rotational motion in question. Thus, statement C is also partially correct.
05

Evaluate Statement D

Finally, let's consider statement D. In rotational motion, every particle of the rigid body indeed moves in a circular path about a line, meaning both the individual particle and the centre of mass of the body undergo an accelerated motion, because their direction is continuously changing. Therefore, statement D is correct. So, the correct statement for the rotational motion of a rigid body is "D: Individual particle and centre of mass of the body undergo an accelerated motion."

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Most popular questions from this chapter

A solid cylinder of mass \(\mathrm{M}\) and \(\mathrm{R}\) is mounted on a frictionless horizontal axle so that it can freely rotate about this axis. A string of negligible mass is wrapped round the cylinder and a body of mass \(\mathrm{m}\) is hung from the string as shown in figure the mass is released from rest then The angular speed of cylinder is proportional to \(\mathrm{h}^{\mathrm{n}}\), where \(\mathrm{h}\) is the height through which mass falls, Then the value of \(n\) is \(\\{\mathrm{A}\\}\) zero \(\\{\mathrm{B}\\} 1\) \(\\{\mathrm{C}\\}(1 / 2)\) \([\mathrm{D}] 2\)

The moment of inertia of a meter scale of mass \(0.6 \mathrm{~kg}\) about an axis perpendicular to the scale and passing through \(30 \mathrm{~cm}\) position on the scale is given by (Breath of scale is negligible). \(\\{\mathrm{A}\\} 0.104 \mathrm{kgm}^{2}\) \\{B \(\\} 0.208 \mathrm{kgm}^{2}\) \(\\{\mathrm{C}\\} 0.074 \mathrm{kgm}^{2}\) \(\\{\mathrm{D}\\} 0.148 \mathrm{kgm}^{2}\)

A circular disc of mass \(\mathrm{m}\) and radius \(\mathrm{r}\) is rolling on a smooth horizontal surface with a constant speed v. Its kinetic energy is \(\\{\mathrm{A}\\}(1 / 4) \mathrm{mv}^{2}\) \(\\{\mathrm{B}\\}(1 / 2) \mathrm{mv}^{2}\) \(\\{\mathrm{C}\\}(3 / 4) \mathrm{mv}^{2}\) \(\\{\mathrm{D}\\} \mathrm{mv}^{2}\)

A thin circular ring of mass \(\mathrm{M}\) and radius \(\mathrm{r}\) is rotating about its axis with a constant angular velocity \(\mathrm{w}\). Two objects each of mass \(\mathrm{m}\) are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity.... $\\{\mathrm{A}\\}[\\{\omega(\mathrm{M}-2 \mathrm{~m})\\} /\\{\mathrm{M}+2 \mathrm{~m}\\}]$ \(\\{\mathrm{B}\\}[\\{\omega \mathrm{M}\\} /\\{\mathrm{M}+2 \mathrm{~m}\\}]\) \(\\{C\\}[\\{\omega M)\\} /\\{M+m\\}]\) \(\\{\mathrm{D}\\}[\\{\omega(\mathrm{M}+2 \mathrm{~m})\\} / \mathrm{M}]\)

The moment of inertia of a uniform circular disc of mass \(\mathrm{M}\) and radius \(\mathrm{R}\) about any of its diameter is \((1 / 4) \mathrm{MR}^{2}\), what is the moment of inertia of the disc about an axis passing through its centre and normal to the disc? \(\\{\mathrm{A}\\} \mathrm{MR}^{2}\) \\{B \(\\}(1 / 2) \mathrm{MR}^{2}\) \(\\{\mathrm{C}\\}(3 / 2) \mathrm{MR}^{2}\) \(\\{\mathrm{D}\\} 2 \mathrm{MR}^{2}\)
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