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A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.
- a)The minimum kinetic energy of the system is 1 joule
- b)The maximum elastic potential energy of the system is 2 joule.
- c)Momentum and total kinetic energy of the system are conserved at every instant.
- d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.
Correct answer is option 'A,B,D'. Can you explain this answer?
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Most Upvoted Answer
A particle moving with kinetic energy = 3 joule makes an elastic head ...
Explanation:
a) The minimum kinetic energy of the system is 1 joule:
In an elastic collision, both momentum and kinetic energy are conserved. Therefore, the total kinetic energy of the system before the collision must be equal to the total kinetic energy of the system after the collision.
Let the initial kinetic energy of the first particle be K1 and the initial kinetic energy of the second particle be K2. Since the first particle has twice the mass of the second particle, the initial kinetic energy of the second particle is half that of the first particle, i.e., K2 = 0.5K1.
During the collision, the first particle transfers some of its kinetic energy to the second particle. Let the final kinetic energy of the first particle be K'1 and the final kinetic energy of the second particle be K'2.
Since this is an elastic collision, both momentum and kinetic energy are conserved. Therefore, we have:
Initial kinetic energy of the system = K1 + K2 = K1 + 0.5K1 = 1.5K1
Final kinetic energy of the system = K'1 + K'2
Since the collision is elastic, the final kinetic energy of the system is equal to the initial kinetic energy of the system. Therefore, K'1 + K'2 = 1.5K1.
Since the first particle transfers some of its kinetic energy to the second particle, the final kinetic energy of the first particle must be less than its initial kinetic energy, i.e., K'1 < k1.="" therefore,="" the="" minimum="" value="" of="" k'1="" is="" />
Substituting K'1 = 0 in the equation K'1 + K'2 = 1.5K1, we get K'2 = 1.5K1. Therefore, the minimum kinetic energy of the system is 1 joule.
b) The maximum elastic potential energy of the system is 2 joule:
In an elastic collision, the maximum elastic potential energy of the system occurs when both particles come to rest momentarily. At this point, all their initial kinetic energy is converted into elastic potential energy.
Let the final kinetic energy of both particles be zero. Therefore, the final kinetic energy of the system is K'1 + K'2 = 0.
Since the collision is elastic, the final kinetic energy of the system is equal to the initial kinetic energy of the system. Therefore, K'1 + K'2 = 1.5K1.
Substituting K'1 + K'2 = 0 in the equation K'1 + K'2 = 1.5K1, we get K'1 = -K'2. Therefore, the maximum value of K'1 and K'2 is when K'1 = K'2 = -0.5K1.
The elastic potential energy of the system is given by the equation: Elastic potential energy = 0.5(K'1)^2 + 0.5(K'2)^2.
Substituting K'1 = K'2 = -0.5K1 in the equation, we get Elastic potential energy = 0.5(-0.5K1)^2 + 0.5(-0.5K1)^2 = 0.5(0.25K1^2 +
a) The minimum kinetic energy of the system is 1 joule:
In an elastic collision, both momentum and kinetic energy are conserved. Therefore, the total kinetic energy of the system before the collision must be equal to the total kinetic energy of the system after the collision.
Let the initial kinetic energy of the first particle be K1 and the initial kinetic energy of the second particle be K2. Since the first particle has twice the mass of the second particle, the initial kinetic energy of the second particle is half that of the first particle, i.e., K2 = 0.5K1.
During the collision, the first particle transfers some of its kinetic energy to the second particle. Let the final kinetic energy of the first particle be K'1 and the final kinetic energy of the second particle be K'2.
Since this is an elastic collision, both momentum and kinetic energy are conserved. Therefore, we have:
Initial kinetic energy of the system = K1 + K2 = K1 + 0.5K1 = 1.5K1
Final kinetic energy of the system = K'1 + K'2
Since the collision is elastic, the final kinetic energy of the system is equal to the initial kinetic energy of the system. Therefore, K'1 + K'2 = 1.5K1.
Since the first particle transfers some of its kinetic energy to the second particle, the final kinetic energy of the first particle must be less than its initial kinetic energy, i.e., K'1 < k1.="" therefore,="" the="" minimum="" value="" of="" k'1="" is="" />
Substituting K'1 = 0 in the equation K'1 + K'2 = 1.5K1, we get K'2 = 1.5K1. Therefore, the minimum kinetic energy of the system is 1 joule.
b) The maximum elastic potential energy of the system is 2 joule:
In an elastic collision, the maximum elastic potential energy of the system occurs when both particles come to rest momentarily. At this point, all their initial kinetic energy is converted into elastic potential energy.
Let the final kinetic energy of both particles be zero. Therefore, the final kinetic energy of the system is K'1 + K'2 = 0.
Since the collision is elastic, the final kinetic energy of the system is equal to the initial kinetic energy of the system. Therefore, K'1 + K'2 = 1.5K1.
Substituting K'1 + K'2 = 0 in the equation K'1 + K'2 = 1.5K1, we get K'1 = -K'2. Therefore, the maximum value of K'1 and K'2 is when K'1 = K'2 = -0.5K1.
The elastic potential energy of the system is given by the equation: Elastic potential energy = 0.5(K'1)^2 + 0.5(K'2)^2.
Substituting K'1 = K'2 = -0.5K1 in the equation, we get Elastic potential energy = 0.5(-0.5K1)^2 + 0.5(-0.5K1)^2 = 0.5(0.25K1^2 +
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A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer?
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A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer?.
A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.a)The minimum kinetic energy of the system is 1 jouleb)The maximum elastic potential energy of the system is 2 joule.c)Momentum and total kinetic energy of the system are conserved at every instant.d)The ratio of kinetic energy to potential energy of the system first decreases and then increases.Correct answer is option 'A,B,D'. Can you explain this answer?.
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