UPSC Exam > UPSC Questions > A particle of mass 10 g moves in a straight l...
Start Learning for Free
A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n?
Most Upvoted Answer
A particle of mass 10 g moves in a straight line with retardation 2x w...
Understanding the Problem
The particle has a mass of 10 g, which is equivalent to 0.01 kg. It experiences a retardation (deceleration) that is proportional to its displacement, described by the equation a = -2x.
Key Concepts to Consider
- Retardation: The force acting on the particle causes it to lose kinetic energy. The retardation is given as a function of displacement: a = -2x.
- Kinetic Energy: The kinetic energy (KE) of the particle can be expressed as KE = (1/2)mv^2, where m is mass and v is velocity.
- Work-Energy Principle: The work done on the particle is equal to the change in kinetic energy. The force can be derived from the retardation.
Calculating the Change in Kinetic Energy
1. Force Calculation: The force acting on the particle can be described as F = ma. Here, m = 0.01 kg and a = -2x. Therefore, F = -0.02x.
2. Work Done: The work done by this force over a displacement x is given by W = ∫F dx = ∫(-0.02x) dx, which evaluates to -0.01x^2.
3. Kinetic Energy Loss: The loss of kinetic energy (ΔKE) can be equated to the work done by the force, resulting in ΔKE = -(-0.01x^2) = 0.01x^2.
4. Comparing with Given Equation: The problem states the loss of kinetic energy is (10/x)^-n J. We can express this as 0.01x^2 = (10/x)^-n.
Finding the Value of n
To match both sides of the equation, we rearrange and analyze the terms:
- Setting 0.01x^2 equal to (10/x)^-n, we can conclude that:
0.01x^2 = 10^n / x^n
This implies:
- n must equal 2 for both sides to match (since 0.01 = 10^-2 and x^2 = x^-n).
Final Conclusion
Thus, the value of n is 2.
The particle has a mass of 10 g, which is equivalent to 0.01 kg. It experiences a retardation (deceleration) that is proportional to its displacement, described by the equation a = -2x.
Key Concepts to Consider
- Retardation: The force acting on the particle causes it to lose kinetic energy. The retardation is given as a function of displacement: a = -2x.
- Kinetic Energy: The kinetic energy (KE) of the particle can be expressed as KE = (1/2)mv^2, where m is mass and v is velocity.
- Work-Energy Principle: The work done on the particle is equal to the change in kinetic energy. The force can be derived from the retardation.
Calculating the Change in Kinetic Energy
1. Force Calculation: The force acting on the particle can be described as F = ma. Here, m = 0.01 kg and a = -2x. Therefore, F = -0.02x.
2. Work Done: The work done by this force over a displacement x is given by W = ∫F dx = ∫(-0.02x) dx, which evaluates to -0.01x^2.
3. Kinetic Energy Loss: The loss of kinetic energy (ΔKE) can be equated to the work done by the force, resulting in ΔKE = -(-0.01x^2) = 0.01x^2.
4. Comparing with Given Equation: The problem states the loss of kinetic energy is (10/x)^-n J. We can express this as 0.01x^2 = (10/x)^-n.
Finding the Value of n
To match both sides of the equation, we rearrange and analyze the terms:
- Setting 0.01x^2 equal to (10/x)^-n, we can conclude that:
0.01x^2 = 10^n / x^n
This implies:
- n must equal 2 for both sides to match (since 0.01 = 10^-2 and x^2 = x^-n).
Final Conclusion
Thus, the value of n is 2.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n?
Question Description
A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n?.
A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n?.
Solutions for A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? defined & explained in the simplest way possible. Besides giving the explanation of
A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n?, a detailed solution for A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? has been provided alongside types of A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? theory, EduRev gives you an
ample number of questions to practice A particle of mass 10 g moves in a straight line with retardation 2x where x us the displacement in si units it's lose of kinetic energy for the above displacement is (10/x)^-n j the value of n? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
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