91Ó°ÊÓ

In column I, nature of collision between two bodies is give while in column II some physical quantity that may remain conserved during the collision is given. Match the entries of column I with the entries of column II. $$ \begin{array}{|l|l|l|} \hline {\text { Column I }} & {\text { Column II }} \\ \hline \text { i. } \quad \text { Elastic collision } & \text { a. } \begin{array}{l} \text { kinetic energy is } \\ \text { conserved } \end{array} \\ \hline \text { ii. } \text { Inelastic collision } & \text { b. } \begin{array}{l} \text { kinetic energy of the } \\ \text { system may increase } \end{array} \\ \hline \begin{array}{l} \text { iii. } \text { Perfectly inelastic } \\ \text { collision } \end{array} & \begin{array}{l} \text { c. } \text { kinetic energy is not } \\ \text { conserved } \end{array} \\ \hline \text { iv. } \begin{array}{l} \text { Collision between two } \\ \text { cars moving at high } \\ \text { speeds } \end{array} & \text { d. } \begin{array}{r} \text { total energy is } \\ \text { conserved } \end{array} \\ \hline \end{array} $$

Step by step solution

01

Analyze Elastic Collisions

For elastic collisions, both momentum and kinetic energy are conserved. Therefore, the statement in Column II that matches is 'kinetic energy is conserved'. So, the correct match is i. Elastic collision with a.

02

Analyze Inelastic Collisions

In inelastic collisions, momentum is conserved but kinetic energy is not. However, the kinetic energy of the system may increase due to external forces or transformations within the system. Therefore, the correct match for ii. Inelastic collision is b.

03

Analyze Perfectly Inelastic Collisions

In perfectly inelastic collisions, the two colliding bodies stick together after the collision, resulting in the loss of kinetic energy. The kinetic energy is not conserved in this case, thus iii. Perfectly inelastic collision matches with c.

04

Analyze High-Speed Car Collisions

When two cars collide at high speeds, it is generally assumed to be an inelastic collision where some energy is transformed into other forms like sound or heat. However, in all collisions, the total energy (including kinetic energy, potential energy, and internal energy) is conserved. Therefore, iv. Collision between two cars moving at high speeds matches with d. Total energy is conserved.

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Key Concepts

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

Elastic Collision

In an elastic collision, two objects collide and then bounce off each other without any permanent deformation or generation of heat. This type of collision is quite theoretical and rarely found in the natural world. However, it is a perfect case to study due to its unique properties. In elastic collisions, two quantities are conserved: momentum and kinetic energy. - **Momentum:** It is the product of the mass and velocity of an object, and it remains constant before and after the collision. - **Kinetic Energy:** This is the energy an object possesses due to its motion, defined as \( \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity. During an elastic collision, the total kinetic energy of the system remains the same before and after the collision.Think of a game of pool, where the billiard balls collide with each other. Ideally, the kinetic energy in pool is nearly conserved because the balls just bounce off each other without sticking together or deforming.

Inelastic Collision

Inelastic collisions differ significantly from elastic ones because the kinetic energy is not conserved, even though the total momentum is conserved. During these collisions, some of the kinetic energy is transformed into other types of energy, such as thermal energy or sound. This energy transformation leads to a decrease in the system's kinetic energy. - **Momentum:** Similar to elastic collisions, momentum is conserved in all inelastic collisions. - **Kinetic Energy:** Not all of the initial kinetic energy is conserved. Some of it is transformed, causing the total kinetic energy after the collision to be less than before. An example of an inelastic collision is a car crash. When two cars collide, the bodies crumple, and a lot of energy is transformed into sound, heat, and deformation of the cars. When referred to simply as 'inelastic', it means that the two objects do not stick together post-collision.

Conservation of Energy

The principle of conservation of energy states that the total energy of a closed system remains constant, although it can change forms. In the context of collisions, this principle can be applied even when kinetic energy is not conserved. - **Total Energy Conservation:** While the kinetic energy may dissipate or reduce, especially in inelastic collisions, the total energy—comprising kinetic, potential, and internal energy—remains constant. - **Energy Transformation:** Energy can be converted, for example, from kinetic energy into sound energy or heat, but the total amount of energy remains the same before and after the collision. Consider a high-speed car crash: though the kinetic energy is diminished due to deformation of the car's body and other factors, the total energy, when all forms are counted, remains conserved. This principle is pivotal in understanding energy flow and transformation in any physical process.