Problem 415 - JEE Physics

Question

Match the column \begin{tabular}{l|l} Column - I & Column - II \end{tabular} (a) Body line on a (p) is a self adjusting horizontal surface \(\quad\) force (b) Static friction (q) is a maximum value of static friction (c) Limiting friction (r) is then limiting friction (d) Dynamic friction (s) force of friction \(=0\) (A) \(\mathrm{a}-\mathrm{s}, \mathrm{b}-\mathrm{p}, \mathrm{c}-\mathrm{q}, \mathrm{d}-\mathrm{r}\) (B) \(\mathrm{a}-\mathrm{p}, \mathrm{b}-\mathrm{q}, \mathrm{c}-\mathrm{r}, \mathrm{d}-\mathrm{s}\) (C) \(\mathrm{a}-\mathrm{s}, \mathrm{b}-\mathrm{r}, \mathrm{c}-\mathrm{q}, \mathrm{d}-\mathrm{p}\) (D) \(\mathrm{a}-\mathrm{r}, \mathrm{b}-\mathrm{q}, \mathrm{c}-\mathrm{p}, \mathrm{d}-\mathrm{s}\)

Step-by-Step Solution

Answer

The short answer is: (A) \(a - s, b - p, c -q, d - r\)

Step 1: Understand each term in Column I

In order to match the terms correctly, we first need to know what each term in Column I means: (a) Body line on a: This term seems incomplete, so we will come back to this once we analyze other terms. (b) Static friction: This is the force that resists the motion of two objects in contact and at rest relative to each other. (c) Limiting friction: The maximum value of static friction that can act between two objects before they start to move relative to each other. (d) Dynamic friction: Also known as kinetic friction, it is the force that resists the relative motion of two objects that are in contact and already in motion. #Step 2: Analyze the terms in Column II#

Step 2: Understand each term in Column II

Now we need to understand what each term in Column II means: (p) Is a self-adjusting horizontal surface force: This could refer to static friction as it adjusts itself to prevent the relative motion between two objects until its maximum value is reached. (q) Is a maximum value of static friction: This clearly refers to the limiting friction. (r) Is then limiting friction: This is a direct reference to limiting friction. (s) Force of friction = 0: This may refer to the condition where there is no frictional force acting on a body. Now going back to term (a), it seems that it might be an error or typo. Since there are no other instructions, we will continue to match the terms with the given options. #Step 3: Match the terms from Column I to Column II#

Step 3: Discover the correct matching pairs

Based on the understanding of each term, we can now match them as follows: (a) Body line on a: Match with (s) because it is the only remaining term. (b) Static friction: Match with (p) because it is a self-adjusting horizontal surface force. (c) Limiting friction: Match with (q) because it is the maximum value of static friction. (d) Dynamic friction: Match with (r) because it is direct reference to limiting friction. #Step 4: Find the corresponding answer choice#

Step 4: Select the answer choice that matches the pairs

The corresponding matching pairs are: \(a - s, b - p, c - q, d - r\) These matches correspond to option (A). Therefore, the correct answer is: (A) \(a - s, b - p, c -q, d - r\)

Key Concepts

Static Friction

Friction is a force that we often encounter in our daily lives. One of its types is static friction, which plays a crucial role in preventing objects from moving when they are at rest. Static friction occurs when two surfaces are in contact but not sliding relative to each other.

This type of friction is self-adjusting. It means that static friction can increase or decrease to exactly match any applied force trying to move the object, up until a certain maximum limit is reached. It keeps the objects stationary as it balances out the applied force.

Consider a book resting on a table. If you gently push it, the static friction counters your push, keeping the book still. However, if you continue to increase the force, there eventually comes a point where static friction is overwhelmed, leading to movement.

Limiting Friction

Limiting friction refers to the maximum value of static friction that can be exerted between two surfaces before motion begins. This is a crucial concept as it marks the threshold beyond which static friction can no longer hold, and movement sets in.

When you push an object, the static friction will increase up to its maximum limit, the limiting friction. If the applied force exceeds this limit, the object begins to slide. This is similar to a dam holding back water—it can do so only up to a certain limit, after which overflow occurs.

The limiting friction is crucial for designing safe surfaces, ensuring that cars can grip the road even when going uphill, and that objects do not slip and fall when placed at an angle.

Dynamic Friction

Once an object begins to move, static friction transitions into a different form called dynamic or kinetic friction. This type of friction acts against the movement of the object, resisting its motion across a surface.

Unlike static friction, dynamic friction has a constant value and does not change with the applied force. It is generally lower than the limiting friction, which is why it is easier to keep an object moving than to start its motion.

Imagine a sled sliding down a snowy hill. The dynamic friction acts between the sled and the snow, slowing it down and eventually bringing it to a stop. The dynamic friction, although lesser than static, still plays a significant role in controlling the speed of moving objects.

Frictional Forces

Frictional forces are vital in physics, forming the opposition that slows down and stops moving objects. These forces arise from the interaction between surface irregularities at a microscopic level. Frictional forces can prevent unwanted movement, making them essential in many practical applications.

There are two main types of frictional forces: static and dynamic. These forces help in everyday activities like driving, walking, or even writing with a pencil. Without friction, these activities would be impossible.

Frictional forces, while often seen as a hindrance, are beneficial. They provide traction, enable brakes in vehicles to function, and allow us to hold objects without them slipping away. Understanding frictional forces helps engineers design better tires, shoes, and machinery that optimally use or counteract friction.