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Two particles are seen to collide and mo...

Two particles are seen to collide and move jointly together after the collision . During such a collision, for the total system,

A

both the mechanical energy and the linear momentum are conserved

B

linear momentum is conserved but not the mechanical energy

C

neither the mechanical energy nor the linear momentum is conserved

D

mechanical energy is conserved but not the linear momentum

Text Solution

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The correct Answer is:
To solve the question, we need to analyze the situation of two particles colliding and moving together after the collision. This type of collision is known as a perfectly inelastic collision. Let's break down the solution step by step: ### Step-by-Step Solution: 1. **Identify the Type of Collision**: - The problem states that two particles collide and then move together. This indicates that they stick together after the collision, which is characteristic of a perfectly inelastic collision. **Hint**: Remember that inelastic collisions involve objects sticking together after impact. 2. **Conservation of Momentum**: - In any collision, the law of conservation of momentum applies. This means that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. - Mathematically, if \( m_1 \) and \( m_2 \) are the masses of the particles and \( u_1 \) and \( u_2 \) are their initial velocities, then: \[ m_1 u_1 + m_2 u_2 = (m_1 + m_2) v \] where \( v \) is the common velocity after the collision. **Hint**: Always check if momentum is conserved in collisions, as it is a fundamental principle. 3. **Mechanical Energy Consideration**: - In perfectly inelastic collisions, some kinetic energy is transformed into other forms of energy (like heat, sound, etc.). Therefore, the total mechanical energy (kinetic energy) is not conserved. - The kinetic energy before the collision is greater than the kinetic energy after the collision. **Hint**: In inelastic collisions, energy is not conserved in the form of mechanical energy, but momentum is. 4. **Evaluating the Options**: - Now, we can evaluate the provided options based on our analysis: - **Option 1**: Both mechanical energy and momentum conserved - **Incorrect** (momentum is conserved, but mechanical energy is not). - **Option 2**: Only momentum is conserved - **Correct** (momentum is conserved, mechanical energy is not). - **Option 3**: Neither mechanical energy nor momentum conserved - **Incorrect** (momentum is conserved). - **Option 4**: Mechanical energy is conserved, but momentum is not - **Incorrect** (momentum is conserved). **Hint**: Always compare your findings with the options provided to identify the correct one. ### Final Answer: The correct option is that only momentum is conserved during the collision, while mechanical energy is not conserved.
To solve the question, we need to analyze the situation of two particles colliding and moving together after the collision. This type of collision is known as a perfectly inelastic collision. Let's break down the solution step by step: ### Step-by-Step Solution: 1. **Identify the Type of Collision**: - The problem states that two particles collide and then move together. This indicates that they stick together after the collision, which is characteristic of a perfectly inelastic collision. **Hint**: Remember that inelastic collisions involve objects sticking together after impact. ...
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Collision is a physical process in which two or more objects, either particle masses or rigid bodies, experience very high force of interaction for a very small duration. It is not essential for the objects to physically touch each other for collision to occur. Irrespective of the nature of interactive force and the nature of colliding bodies, Newton's second law holds good on the system. Hence, momentum of the system before and after the collision remains conserved if no appreciable external force acts on the system during collision. The amount of energy loss during collision, if at all, is indeed dependent on the nature of colliding objects. The energy loss is observed to be maximum when objects stick together after collision. The terminology is to define collision as 'elastic' if no energy loss takes place and to define collision as 'plastic' for maximum energy loss. The behaviour of system after collision depends on the position of colliding objects as well. A unidirectional motion of colliding objects before collision can turn into two dimensional after collision if the line joining the centre of mass of the two colliding objects is not parallel to the direction of velocity of each particle before collision. Such type of collision is referred to as oblique collision which may be either two or three dimensional. For which of the following collisions, the external force acting on the system during collision is not appreciable as mentioned in paragraph 1.

Collision is a physical process in which two or more objects, either particle masses or rigid bodies, experience very high force of interaction for a very small duration. It is not essential for the objects to physically touch each other for collision to occur. Irrespective of the nature of interactive force and the nature of colliding bodies, Newton's second law holds good on the system. Hence, momentum of the system before and after the collision remains conserved if no appreciable external force acts on the system during collision. The amount of energy loss during collision, if at all, is indeed dependent on the nature of colliding objects. The energy loss is observed to be maximum when objects stick together after collision. The terminology is to define collision as 'elastic' if no energy loss takes place and to define collision as 'plastic' for maximum energy loss. The behaviour of system after collision depends on the position of colliding objects as well. A unidirectional motion of colliding objects before collision can turn into two dimensional after collision if the line joining the centre of mass of the two colliding objects is not parallel to the direction of velocity of each particle before collision. Such type of collision is referred to as oblique collision which may be either two or three dimensional. According to the definition of collision in paragraph I, which of the following physical process is not a collision?

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