Problem 632 - JEE Physics

Question

Statement \(-1\) - Friction is necessary for a body to roll on surface. Statement \(-2\) - Friction provides the necessary tangential force and torque. \(\\{\mathrm{A}\\}\) Statement \(-1\) is correct (true), Statement \(-2\) is true and Statement- 2 is correct explanation for Statement \(-1\) \(\\{B\\}\) Statement \(-1\) is true, statement \(-2\) is true but statement- 2 is not the correct explanation four statement \(-1\). \(\\{\mathrm{C}\\}\) Statement \(-1\) is true, statement \(-2\) is false \\{D \\} Statement- 2 is false, statement \(-2\) is true

Step-by-Step Solution

Answer

Option A: Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation for Statement 1.

Step 1: Understanding Statement 1

Statement 1 claims that friction is necessary for a body to roll on a surface. This statement is accurate, as without friction, the body would not be able to grip the surface and initiate rolling motion. This implies that Statement 1 is true.

Step 2: Understanding Statement 2

Statement 2 asserts that friction provides the necessary tangential force and torque. This statement is also accurate. When a body rolls on a surface, the force of friction acts tangentially. The torque generated by this frictional force allows the body to rotate and maintain its rolling motion. Thus, Statement 2 is true as well.

Step 3: Evaluating the Relationship Between Statement 1 and Statement 2

Since Statement 2 explains the mechanism by which friction plays a significant role in a body's ability to roll on a surface, we can conclude that it is the correct explanation for Statement 1.

Step 4: Selecting the Correct Option

Based on our reasoning and explanation, Option A is the correct one: Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation for Statement 1.

Key Concepts

Tangential Force

In the context of rolling motion, tangential force plays a pivotal role. Imagine a wheel trying to move over a flat surface. The force that acts along the surface line or at a tangent to the wheel’s bottom is termed the tangential force.
It arises due to friction, which opposes the sliding motion.
Friction here doesn’t just hold the wheel back; it cleverly transforms into a force that helps it roll forward smoothly. Without this force, the wheel would simply slide, unable to grip the surface properly.
Thus, tangential force becomes essential for accelerating or decelerating a rolling body.

• Friction acts along the point of contact.
• It provides a direction for motion.
• Crucial for initiating and maintaining rolling.

Understanding tangential force is essential, as it indicates how surfaces interact frictionally to allow rolling action.

Torque

Torque is the force that causes an object to rotate around an axis. Think of it as the "twisting" or "turning" force that propels a wheel into a spin. In physics, torque is what makes the rolling motion possible.
Friction provides the necessary torque when a rolling object is in contact with a surface.
To visualize, consider pushing a door; the further from the hinge you push, the easier it is to open. That's torque in action: force applied at a distance from the center of rotation.The formula for torque (\( \tau \)) is given by:\[ \tau = F \times r \]Where:

• \( F \) is the force applied.
• \( r \) is the distance from the pivot point.

Frictional torque is crucial since it determines how quickly or efficiently an object can start, stop, or change its rolling speed.

Rolling Motion

Rolling motion is a combination of rotation and translation. It occurs when an object like a wheel or a ball moves along a surface, rolling rather than sliding. Imagine a bicycle wheel smoothly moving along the road; it's a classic example of rolling motion.
For an object to roll without slipping, the condition is that the linear velocity at the point of contact with the surface should be zero.
This means that rolling occurs when the tangential speed at the contact point equals the body's translational speed. Some key aspects include:

• Rotational motion around the wheel’s axis.
• Linear motion corresponding to the wheel’s travel across the ground.
• Friction acts to initiate rolling and maintains it without slipping.

Understanding the synergy of these motions helps explain why friction is so vital in rolling, ensuring that rotation translates effectively into forward movement.