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Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]
- a)1 : 2
- b)1 : 1
- c)4 : 1
- d)1 : 4
Correct answer is option 'D'. Can you explain this answer?
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Two bodies with kinetic energies in the r atio 4 : 1 are moving with e...
[Given: p1=p2]
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Two bodies with kinetic energies in the r atio 4 : 1 are moving with e...
Understanding Kinetic Energy and Momentum
To solve the problem, we start by defining the kinetic energy (KE) and momentum (p) formulas:
- Kinetic Energy (KE): KE = 1/2 mv²
- Momentum (p): p = mv
Given that two bodies have kinetic energies in the ratio of 4:1 and move with equal linear momentum, we can denote:
- Mass of body 1: m1
- Mass of body 2: m2
- Velocity of body 1: v1
- Velocity of body 2: v2
Setting Up the Ratio of Kinetic Energies
Since the kinetic energies are in the ratio 4:1, we can write:
- KE1 / KE2 = 4 / 1
This leads us to:
- (1/2)m1v1² / (1/2)m2v2² = 4 / 1
Which simplifies to:
- (m1v1²) / (m2v2²) = 4 / 1
Using Equal Momentum
Given that both bodies have equal momentum, we have:
- m1v1 = m2v2
From this, we can express v2 in terms of v1:
- v2 = (m1/m2)v1
Substituting for Velocity
Now, substitute v2 into the kinetic energy ratio:
- m1v1² / m2((m1/m2)v1)² = 4 / 1
This simplifies to:
- m1v1² / (m2(m1²/m2²)v1²) = 4 / 1
Which further simplifies to:
- m2/m1 = 4 / 1
Conclusion: Mass Ratio
Rearranging gives us:
- m1/m2 = 1/4
Thus, the ratio of their masses is 1:4, confirming that the correct answer is option 'D'.
To solve the problem, we start by defining the kinetic energy (KE) and momentum (p) formulas:
- Kinetic Energy (KE): KE = 1/2 mv²
- Momentum (p): p = mv
Given that two bodies have kinetic energies in the ratio of 4:1 and move with equal linear momentum, we can denote:
- Mass of body 1: m1
- Mass of body 2: m2
- Velocity of body 1: v1
- Velocity of body 2: v2
Setting Up the Ratio of Kinetic Energies
Since the kinetic energies are in the ratio 4:1, we can write:
- KE1 / KE2 = 4 / 1
This leads us to:
- (1/2)m1v1² / (1/2)m2v2² = 4 / 1
Which simplifies to:
- (m1v1²) / (m2v2²) = 4 / 1
Using Equal Momentum
Given that both bodies have equal momentum, we have:
- m1v1 = m2v2
From this, we can express v2 in terms of v1:
- v2 = (m1/m2)v1
Substituting for Velocity
Now, substitute v2 into the kinetic energy ratio:
- m1v1² / m2((m1/m2)v1)² = 4 / 1
This simplifies to:
- m1v1² / (m2(m1²/m2²)v1²) = 4 / 1
Which further simplifies to:
- m2/m1 = 4 / 1
Conclusion: Mass Ratio
Rearranging gives us:
- m1/m2 = 1/4
Thus, the ratio of their masses is 1:4, confirming that the correct answer is option 'D'.
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Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer?.
Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two bodies with kinetic energies in the r atio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [1999]a)1 : 2b)1 : 1c)4 : 1d)1 : 4Correct answer is option 'D'. Can you explain this answer?.
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