The Question is from neet-physics laws-of-motion , and it was created by the author VENKATESWARARAO

Question

Two identical billiard balls collide elastically.  If one ball was initially at rest, what happens to the momentum of the moving ball after the collision?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
**Primary Concept**: Conservation of Momentum and Kinetic Energy in Elastic Collisions
**Related Topics**: Momentum, Kinetic Energy, Elastic Collision, Impulse
**Prerequisites**: Understanding of momentum, kinetic energy, and the concept of elastic collisions.
## SOLUTION PATHWAY
**Given Information**:
*   Two identical billiard balls (same mass).
*   One ball is initially at rest.
*   The collision is elastic (both momentum and kinetic energy are conserved).
**Method & Steps**:
1.  **Initial Momentum:** The initial momentum of the system is entirely due to the moving ball. Let's denote the mass of each ball as $m$ and the initial velocity of the moving ball as $v_i$. The initial momentum of the system, $P_i$, is then $P_i = mv_i$.
    Reasoning: The ball at rest has zero momentum, and the total momentum is the sum of individual momenta.
    Formula/Rule: $P = mv$
2.  **Final Momentum:** In an elastic collision, both momentum and kinetic energy are conserved. For identical masses with one initially at rest, the moving ball comes to rest and the initially resting ball moves with the initial velocity of the moving ball. So, the final momentum of the system, $P_f$, is now solely due to the other ball, $P_f = mv_i$.
    Working:  If we denote the final velocities as $v_{1f}$ and $v_{2f}$, the conservation of momentum gives $mv_i = mv_{1f} + mv_{2f}$.  For identical mass with one initially at rest, $v_{1f} = 0$ and $v_{2f} = v_i$.
     Key Point: In an elastic collision between two equal masses, if one is initially at rest, the moving ball stops and transfers all its momentum to the other ball.
3.  **Change in Momentum:** The initial momentum of the moving ball was $mv_i$, and its final momentum is 0. Therefore, the momentum of the moving ball has been completely transferred to the other ball. The total momentum remains $mv_i$.
    Result:  The momentum of the moving ball is completely transferred to the other ball.
    Verification: Conservation of momentum is satisfied, as the total momentum before and after the collision is $mv_i$.
## OPTION ANALYSIS
[A] :x: It is doubled. This is incorrect because the momentum is transferred, not doubled.
[B] :x: It becomes zero. This is correct for the moving ball's momentum, but not the system's momentum. This option is incomplete for the question.
[C] ✓: It is completely transferred to the other ball. This is correct because the initially moving ball stops and gives all of its momentum to the other ball.
[D] :x: It remains unchanged. This is incorrect because the moving ball's momentum changes, though the total momentum of the system remains constant.
## LEARNING AIDS
**Common Mistakes**:
1.  **Confusing momentum and kinetic energy:** Momentum is a vector, and kinetic energy is a scalar. Both are conserved in elastic collisions, but they behave differently.
    How to avoid: Remember that momentum is a vector and is conserved in any collision. Kinetic energy is a scalar and is conserved only in elastic collisions.
2.  **Assuming momentum is always conserved for each object individually:** Momentum is conserved for the system as a whole, not necessarily for each individual object.
    How to avoid: Always consider the total momentum of the system, not just the momentum of a single object.
**Quick Tips**:
1.  **For equal mass elastic collisions:** When two equal masses collide elastically and one is initially at rest, the moving mass stops, and the other mass starts moving with the velocity of the first.
2.  **Visualize the collision:** Drawing a quick diagram of the before and after scenario can help understand the momentum transfer.

VENKATESWARARAO · Answer

It is doubled.

VENKATESWARARAO · Answer

It becomes zero.

VENKATESWARARAO · Answer

The correct Option is "It is completely transferred to the other ball."

VENKATESWARARAO · Answer

It remains unchanged.

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