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A ball moving with speed ν hits another identical ball at rest, The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is
- a)ν2/4S
- b)ν2/8S
- c)ν2/2S
- d)ν2/S
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A ball moving with speed ν hits another identical ball at rest, The...
By conservation of momentum, final velocity=v/2
And by energy conservation,
Initial K.E=Final K.E+heat
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
A ball moving with speed ν hits another identical ball at rest, The...
Explanation:
- Initial Kinetic Energy:
- The initial kinetic energy of the first ball is given by 1/2 mv^2, where m is the mass of each ball and v is the speed of the first ball.
- The initial kinetic energy of the second ball is 0 as it is at rest.
- Final Kinetic Energy:
- After collision, the two balls stick together and move with a common velocity.
- The final kinetic energy of the combined system is given by 1/2 (2m)(v^2/2) = mv^2/2.
- Change in Kinetic Energy:
- The change in kinetic energy is the difference between the final and initial kinetic energies:
- ΔKE = mv^2/2 - 1/2 mv^2 = mv^2/2 - mv^2/2 = 0.
- Heat Generated:
- The entire change in kinetic energy is converted into heat. According to the formula for heat generated, Q = ΔKE = 0.
- Temperature Rise:
- The formula for temperature rise due to heat generated is given by Q = mcΔT, where m is the mass, c is the specific heat, and ΔT is the temperature rise.
- Since Q = 0, we have 0 = mcΔT, which implies that the temperature rise ΔT = 0.
- Conclusion:
- Therefore, the temperature rise resulting from the collision is 0.
Therefore, option 'b) ν^2/8S' is the correct answer.
- Initial Kinetic Energy:
- The initial kinetic energy of the first ball is given by 1/2 mv^2, where m is the mass of each ball and v is the speed of the first ball.
- The initial kinetic energy of the second ball is 0 as it is at rest.
- Final Kinetic Energy:
- After collision, the two balls stick together and move with a common velocity.
- The final kinetic energy of the combined system is given by 1/2 (2m)(v^2/2) = mv^2/2.
- Change in Kinetic Energy:
- The change in kinetic energy is the difference between the final and initial kinetic energies:
- ΔKE = mv^2/2 - 1/2 mv^2 = mv^2/2 - mv^2/2 = 0.
- Heat Generated:
- The entire change in kinetic energy is converted into heat. According to the formula for heat generated, Q = ΔKE = 0.
- Temperature Rise:
- The formula for temperature rise due to heat generated is given by Q = mcΔT, where m is the mass, c is the specific heat, and ΔT is the temperature rise.
- Since Q = 0, we have 0 = mcΔT, which implies that the temperature rise ΔT = 0.
- Conclusion:
- Therefore, the temperature rise resulting from the collision is 0.
Therefore, option 'b) ν^2/8S' is the correct answer.
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A ball moving with speed ν hits another identical ball at rest, The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision isa)ν2/4Sb)ν2/8Sc)ν2/2Sd)ν2/SCorrect answer is option 'B'. Can you explain this answer?
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