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91Ó°ÊÓ

Mark correct option or options: (a) Rolling friction always oppose the motion of centre of mass of rolling body (b) Sliding friction always oppose the motion of centre of mass of rolling body (c) Rolling friction depends upon hardness of the surface (d) Rolling friction does not depend upon roughness of the surface (e) (a), (c) and (d) are correct

Short Answer

Expert verified
Option (e): (a), (c), and (d) are correct.

Step by step solution

01

Analyze Option (a)

Rolling friction is the resistive force that slows down the motion of a rolling object on a surface. It acts at the point of contact in the direction opposite to movement of the center of mass. Therefore, option (a) is correct.
02

Analyze Option (b)

Sliding friction occurs when an object slides across a surface. It opposes the relative motion or tendency of such motion. However, for a rolling body, sliding friction is not typically relevant unless the object is sliding rather than rolling. Therefore, option (b) is incorrect as it specifically refers to sliding friction opposing motion of the center of mass in rolling bodies.
03

Analyze Option (c)

Rolling friction does depend on the hardness of the surface. Harder surfaces tend to reduce the deformation at the point of contact, thus decreasing rolling friction. Therefore, option (c) is correct.
04

Analyze Option (d)

Rolling friction is not significantly affected by the roughness of surfaces because deformation at the contact point plays a larger role. Hence, option (d) is correct.
05

Verify Option (e)

Since options (a), (c), and (d) have been determined to be correct through logical analysis, option (e) is indeed correct as it states that options (a), (c), and (d) are correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rolling Friction
Rolling friction is the resistance encountered by an object when it rolls over a surface. It acts at the point of contact between the rolling body and the surface. This force always works opposite to the direction of motion of the center of mass, effectively slowing down the object. Rolling friction is significantly lower than sliding friction, which is why wheels and ball bearings are used to make movement smoother and require less effort. When analyzing real-world applications, you will notice that rolling friction is crucial for vehicles, machinery, and any appliance involving moving parts structured for rotation or circulation, as it reduces energy loss during motion.
Sliding Friction
Sliding friction occurs when there is a relative movement or sliding between two surfaces. This force is known for opposing the direction of movement. It is generally larger than rolling friction, causing more energy dissipation in the form of heat. When you push a book across a table, the resistive force you feel is sliding friction. In the context of rolling objects, sliding friction makes an appearance if the object begins to slip or skid rather than continuing its roll. This concept elucidates why conditions like proper tire inflation and tread design are crucial to avoiding slips, as these factors help maintain grip, minimizing unwanted sliding.
Hardness and Surface Interaction
The hardness of a surface significantly impacts rolling friction. Hard surfaces tend to deform less under pressure compared to softer surfaces. Since rolling friction arises mainly due to the deformation at the point of contact, a harder surface will generally lead to reduced resistance. For instance, a billiard ball on a pool table rolls much more effortlessly than on a soft carpet. The interaction between the hardness of surfaces and rolling objects is vital in determining how easily an object rolls. Therefore, for optimal performance and reduced energy consumption, selecting materials with appropriate hardness becomes crucial in design settings like sports equipment, manufacturing, and transport industries.
Motion of Center of Mass
The motion of the center of mass plays a pivotal role in the dynamics of objects, particularly when discussing friction. The center of mass is the point where you can consider the entire mass of an object to be concentrated. Even in complex structures, understanding this motion helps predict behavior under various forces. For instance, in a rolling sphere or a bike moving down a road, the center of mass follows a trajectory determined by forces such as gravity, friction, and any applied forces. Friction, whether rolling or sliding, predominantly acts to oppose the movement of this center. Understanding the motion of the center of mass is fundamental to mastering concepts in dynamics, aiding engineers and designers in innovations and efficiencies across numerous technological fields.

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Most popular questions from this chapter

In a radioactive decay, a number of fragments are found. If parent nucleus is initially at rest then after decay centre of mass will : (a) move on a straight line (b) move in a circle (c) remain in rest (d) move in parabolic path

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