JEE Exam > JEE Questions > A point mass of 1 kg collides elastically wit...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
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?
Question Description
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.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup