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A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:
- a)0, 1
- b)1, 1 [2010]
- c)1, 0.5
- d)0, 2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A ball moving with velocity 2 m/s collides head on with another statio...
By conservation of momentum, 2m = mv1' + 2mv2' ... (ii) From (i),
From (ii), 2 = v1'+ 2 + 2 v1'
⇒ v1 = 0 and v2 = 1 ms–1
Most Upvoted Answer
A ball moving with velocity 2 m/s collides head on with another statio...
Given:
- Initial velocity of first ball (u1) = 2 m/s
- Initial velocity of second ball (u2) = 0 m/s (stationary)
- Mass of second ball (m2) = 2m (double the mass of first ball)
- Coefficient of restitution (e) = 0.5
To find:
- Final velocities of both balls (v1 and v2) after collision
Solution:
1. Using conservation of momentum:
- Before collision, total momentum = m1u1 + m2u2 = m1(2) + m2(0) = 2m1
- After collision, total momentum = m1v1 + m2v2
2. Using coefficient of restitution:
- e = (relative velocity of separation) / (relative velocity of approach)
- For a head-on collision, relative velocity of approach = u1 - u2 = 2 m/s
- Therefore, relative velocity of separation = e * (u1 - u2) = 0.5 * 2 = 1 m/s
3. Using conservation of energy:
- Kinetic energy before collision = (1/2) * m1 * u1^2 + (1/2) * m2 * u2^2 = m1
- Kinetic energy after collision = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
4. Solving for v1 and v2:
- From step 1, m1u1 + m2u2 = m1v1 + m2v2
- Since m2 = 2m1, we can simplify the equation as:
m1u1 = m1v1 + 2m1v2
u1 = v1 + 2v2
- Substituting u1 in terms of v1 and v2:
2 = v1 + 2v2 + 2v2
v1 + 4v2 = 2
- From step 3, we can simplify the kinetic energy equation as:
m1 = (1/2) * m1 * v1^2 + m2 * v2^2
1 = (1/2) * v1^2 + 2v2^2
- Rearranging the equations and solving simultaneously:
v1 = 0 m/s
v2 = 1 m/s
Therefore, the final velocities of the two balls after collision are 0 m/s and 1 m/s respectively. Hence, the correct answer is option A.
- Initial velocity of first ball (u1) = 2 m/s
- Initial velocity of second ball (u2) = 0 m/s (stationary)
- Mass of second ball (m2) = 2m (double the mass of first ball)
- Coefficient of restitution (e) = 0.5
To find:
- Final velocities of both balls (v1 and v2) after collision
Solution:
1. Using conservation of momentum:
- Before collision, total momentum = m1u1 + m2u2 = m1(2) + m2(0) = 2m1
- After collision, total momentum = m1v1 + m2v2
2. Using coefficient of restitution:
- e = (relative velocity of separation) / (relative velocity of approach)
- For a head-on collision, relative velocity of approach = u1 - u2 = 2 m/s
- Therefore, relative velocity of separation = e * (u1 - u2) = 0.5 * 2 = 1 m/s
3. Using conservation of energy:
- Kinetic energy before collision = (1/2) * m1 * u1^2 + (1/2) * m2 * u2^2 = m1
- Kinetic energy after collision = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
4. Solving for v1 and v2:
- From step 1, m1u1 + m2u2 = m1v1 + m2v2
- Since m2 = 2m1, we can simplify the equation as:
m1u1 = m1v1 + 2m1v2
u1 = v1 + 2v2
- Substituting u1 in terms of v1 and v2:
2 = v1 + 2v2 + 2v2
v1 + 4v2 = 2
- From step 3, we can simplify the kinetic energy equation as:
m1 = (1/2) * m1 * v1^2 + m2 * v2^2
1 = (1/2) * v1^2 + 2v2^2
- Rearranging the equations and solving simultaneously:
v1 = 0 m/s
v2 = 1 m/s
Therefore, the final velocities of the two balls after collision are 0 m/s and 1 m/s respectively. Hence, the correct answer is option A.
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A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer?
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A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer?.
A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be:a)0, 1b)1, 1 [2010]c)1, 0.5d)0, 2Correct answer is option 'A'. Can you explain this answer?.
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