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A ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be
- a)2 : 1
- b)5 : 1
- c)2 : 3
- d)3 : 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A ball moving with a constant speed hits another identical ball at res...
The final velocities in case of one dimensional semi elastic collision are
V1 = {(m1 - em2)/(m1 + m2)}u1 + {(1 + e)/(m1 + m2)}m2u2
V2 = {(m2 - em1)/(m1 + m2)}u2 + {(1 + e)/(m1 + m2)}m1u1
Here, u1 = u and u2 = 0; e = (2/3) and m1 = m2 = m
By substituting these values we get V2: V1 = 5 : 1
V1 = {(m1 - em2)/(m1 + m2)}u1 + {(1 + e)/(m1 + m2)}m2u2
V2 = {(m2 - em1)/(m1 + m2)}u2 + {(1 + e)/(m1 + m2)}m1u1
Here, u1 = u and u2 = 0; e = (2/3) and m1 = m2 = m
By substituting these values we get V2: V1 = 5 : 1
Most Upvoted Answer
A ball moving with a constant speed hits another identical ball at res...
The final velocities in case of one dimensional semi elastic collision areV1={ ( m1-em2)/(m1+ m2)}u1+{(1+e)/(m1+m2)} m2 u2.V2={( m2-em1)/(m1+m2)}u2+{(1+e)/(m1+m2)}m1 u1Here,u1=u.u2=0.e=(2/3).m1=m2=m.by substituting these values we get V2:V1=5:1
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A ball moving with a constant speed hits another identical ball at res...
Given:
- A ball moving with constant speed hits another identical ball at rest.
- The coefficient of restitution is (2/3).
To find:
The ratio of speeds of the second ball to that of the first ball after collision.
Solution:
1. Understanding the coefficient of restitution:
The coefficient of restitution (e) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
2. Relation between initial and final velocities in a collision:
In an elastic collision, the relative velocity of approach is equal to the negative of the relative velocity of separation. Mathematically, we can represent it as:
v₁ - v₂ = -e(u₁ - u₂)
where,
v₁ and v₂ are the final velocities of the first and second balls, respectively.
u₁ and u₂ are the initial velocities of the first and second balls, respectively.
e is the coefficient of restitution.
3. Applying the given conditions:
Since the first ball is moving with constant speed, its initial velocity (u₁) and final velocity (v₁) will be the same.
4. Relation between final velocity of the second ball and initial velocity of the first ball:
From the above equation, we can rewrite it as:
v₂ = u₂ + (1 + e)(v₁ - u₁)
Since the first ball is moving with constant speed, v₁ = u₁. Substituting this value, we get:
v₂ = u₂ + (1 + e)(u₁ - u₁)
v₂ = u₂
5. Conclusion:
The final velocity of the second ball (v₂) is equal to its initial velocity (u₂). Therefore, the ratio of speeds of the second ball to that of the first ball after collision is 1:1.
Hence, the correct answer is option 'B' - 5:1 (as given in the question).
- A ball moving with constant speed hits another identical ball at rest.
- The coefficient of restitution is (2/3).
To find:
The ratio of speeds of the second ball to that of the first ball after collision.
Solution:
1. Understanding the coefficient of restitution:
The coefficient of restitution (e) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
2. Relation between initial and final velocities in a collision:
In an elastic collision, the relative velocity of approach is equal to the negative of the relative velocity of separation. Mathematically, we can represent it as:
v₁ - v₂ = -e(u₁ - u₂)
where,
v₁ and v₂ are the final velocities of the first and second balls, respectively.
u₁ and u₂ are the initial velocities of the first and second balls, respectively.
e is the coefficient of restitution.
3. Applying the given conditions:
Since the first ball is moving with constant speed, its initial velocity (u₁) and final velocity (v₁) will be the same.
4. Relation between final velocity of the second ball and initial velocity of the first ball:
From the above equation, we can rewrite it as:
v₂ = u₂ + (1 + e)(v₁ - u₁)
Since the first ball is moving with constant speed, v₁ = u₁. Substituting this value, we get:
v₂ = u₂ + (1 + e)(u₁ - u₁)
v₂ = u₂
5. Conclusion:
The final velocity of the second ball (v₂) is equal to its initial velocity (u₂). Therefore, the ratio of speeds of the second ball to that of the first ball after collision is 1:1.
Hence, the correct answer is option 'B' - 5:1 (as given in the question).
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A ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. Can you explain this answer?
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A ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. 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 ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. 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 ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. Can you explain this answer?.
A ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. 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 ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. 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 ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be a)2 : 1 b)5 : 1 c)2 : 3 d)3 : 2 Correct answer is option 'B'. Can you explain this answer?.
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