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A body of mass m is moving with a linear velocity of v m/s and collides with a stationary wall elastically. The coefficient of restitution for the collision was 0.8. If after the collision, the body of mass m starts moving back on its original path and the wall remains at rest, then the return velocity of the body of mass m will be
  • a)
    -0.2v m/s
  • b)
    -0.8v m/s
  • c)
    0.2v m/s
  • d)
    0.8v m/s
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A body of mass m is moving with a linear velocity of v m/s and collide...
Explanation:

Given:
- Mass of the body, m
- Initial velocity of the body, v m/s
- Coefficient of restitution, e = 0.8

Understanding Elastic Collision:
- In an elastic collision, both momentum and kinetic energy are conserved.
- The coefficient of restitution, e, is the ratio of relative velocities after and before the collision.

Applying Conservation of Momentum:
- Initial momentum = Final momentum
- m * v = m * (-v') [negative sign indicates the direction is opposite]
- v' = -v

Applying Coefficient of Restitution:
- e = (relative velocity after collision) / (relative velocity before collision)
- 0.8 = (v' - 0) / (v - 0)
- 0.8 = (-v) / v
- 0.8 = -1
- v = -1 * 0.8
- v = -0.8v

Conclusion:
- The return velocity of the body after the collision is -0.8v m/s, which means the body moves back with a velocity of 0.8 times the initial velocity in the opposite direction. Hence, the correct answer is option B: -0.8v m/s.
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Community Answer
A body of mass m is moving with a linear velocity of v m/s and collide...
Relative velocity of object approaching the wall = v - 0 = v m/s
Relative velocity of separation of object = 0 - u
Coefficient of restitution = 0.8
Therefore,

Therefore, the return velocity of the ball = -0.8v m/s
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A body of mass m is moving with a linear velocity of v m/s and collides with a stationary wall elastically. The coefficient of restitution for the collision was 0.8. If after the collision, the body of mass m starts moving back on its original path and the wall remains at rest, then the return velocity of the body of mass m will bea)-0.2v m/sb)-0.8v m/sc)0.2v m/sd)0.8v m/sCorrect answer is option 'B'. Can you explain this answer?
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