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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?
- a)Total momentum of the system is 3 kg ms–1
- b)Momentum of 5 kg mass after collision is 4 kg ms–1
- c)Kinetic energy of the centre of mass is 0.75 J
- d)Total kinetic energy of the system is 4J
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
A point mass of 1 kg collides elastically with a stationary point mass...
According to law of conservation of linear momentum 1 × u1 + 5 × 0 = 1 (–2) + 5 (v2)
⇒ u1 = – 2 + 5 v2 ...(i)
⇒ u1 = – 2 + 5 v2 ...(i)
The coefficient of restituition
On solving (i) & (ii) we get desired results.
Most Upvoted Answer
A point mass of 1 kg collides elastically with a stationary point mass...
To solve this problem, we can use the principle of conservation of momentum and the principle of conservation of kinetic energy.
Let's denote the initial velocity of the 1 kg mass as v1i and the initial velocity of the 5 kg mass as v2i. Since the 5 kg mass is stationary, its initial velocity is 0 (v2i = 0).
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be written as:
m1 * v1i + m2 * v2i = m1 * v1f + m2 * v2f
where m1 and m2 are the masses of the two objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.
Substituting the given values, we get:
1 kg * v1i + 5 kg * 0 = 1 kg * (-2 m/s) + 5 kg * v2f
Simplifying the equation, we have:
v1i = -2 m/s + 5 kg * v2f
Now, let's use the principle of conservation of kinetic energy. The total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, this can be written as:
0.5 * m1 * v1i^2 + 0.5 * m2 * v2i^2 = 0.5 * m1 * v1f^2 + 0.5 * m2 * v2f^2
Substituting the given values and rearranging the equation, we have:
0.5 * 1 kg * (-2 m/s)^2 + 0.5 * 5 kg * 0 = 0.5 * 1 kg * (2 m/s)^2 + 0.5 * 5 kg * v2f^2
Simplifying the equation, we get:
2 J = 2 J + 0.5 * 5 kg * v2f^2
Subtracting 2 J from both sides, we have:
0 = 0.5 * 5 kg * v2f^2
0 = 2.5 kg * v2f^2
Since the mass cannot be zero, the only solution is v2f = 0.
Therefore, after the collision, the 5 kg mass remains at rest and the 1 kg mass reverses its direction and moves with a speed of 2 m/s.
Let's denote the initial velocity of the 1 kg mass as v1i and the initial velocity of the 5 kg mass as v2i. Since the 5 kg mass is stationary, its initial velocity is 0 (v2i = 0).
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be written as:
m1 * v1i + m2 * v2i = m1 * v1f + m2 * v2f
where m1 and m2 are the masses of the two objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.
Substituting the given values, we get:
1 kg * v1i + 5 kg * 0 = 1 kg * (-2 m/s) + 5 kg * v2f
Simplifying the equation, we have:
v1i = -2 m/s + 5 kg * v2f
Now, let's use the principle of conservation of kinetic energy. The total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, this can be written as:
0.5 * m1 * v1i^2 + 0.5 * m2 * v2i^2 = 0.5 * m1 * v1f^2 + 0.5 * m2 * v2f^2
Substituting the given values and rearranging the equation, we have:
0.5 * 1 kg * (-2 m/s)^2 + 0.5 * 5 kg * 0 = 0.5 * 1 kg * (2 m/s)^2 + 0.5 * 5 kg * v2f^2
Simplifying the equation, we get:
2 J = 2 J + 0.5 * 5 kg * v2f^2
Subtracting 2 J from both sides, we have:
0 = 0.5 * 5 kg * v2f^2
0 = 2.5 kg * v2f^2
Since the mass cannot be zero, the only solution is v2f = 0.
Therefore, after the collision, the 5 kg mass remains at rest and the 1 kg mass reverses its direction and moves with a speed of 2 m/s.
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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer?
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A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer?.
A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer?.
Solutions for A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses?a)Total momentum of the system is 3 kg ms–1b)Momentum of 5 kg mass after collision is 4 kg ms–1c)Kinetic energy of the centre of mass is 0.75 Jd)Total kinetic energy of the system is 4JCorrect answer is option 'A,C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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