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Two balls each of mass 2kg (one at rest)...

Two balls each of mass 2kg (one at rest) undergo oblique collision is perfectly elastic, then the angle between their velocities after collision is

A

30°

B

60°

C

45°

D

90°

Text Solution

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The correct Answer is:
To solve the problem of finding the angle between the velocities of two balls after an oblique elastic collision, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Problem**: We have two balls, each with a mass of 2 kg. One ball is initially at rest, and they undergo an oblique collision that is perfectly elastic. We need to find the angle between their velocities after the collision. 2. **Define Elastic Collision**: In a perfectly elastic collision, both momentum and kinetic energy are conserved. However, for this specific problem, we will focus on the relationship between the angles after the collision. 3. **Use the Property of Elastic Collisions**: For two objects colliding elastically, if one object is at rest, the angle between their velocities after the collision is related to the angles of incidence and reflection. Specifically, it is a known result that the sum of the angles of the two objects after the collision is 90 degrees. 4. **Apply the Angle Relationship**: Let’s denote the angles of the two balls after the collision as θ₁ and θ₂. According to the property of elastic collisions: \[ θ₁ + θ₂ = 90^\circ \] 5. **Conclusion**: Since the angle between the two velocities after the collision must sum to 90 degrees, we conclude that the angle between their velocities after the collision is 90 degrees. ### Final Answer: The angle between their velocities after the collision is **90 degrees**.
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