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A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be?
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A particle of mass 2kg is moves on the x-axis under influence of force...
Solution:
Given: Mass of particle (m) = 2 kg
Initial position (x1) = 4 cm = 0.04 m
Final position (x2) = 2 m
Force of attraction (F) = -4/x^2
To find: Speed of particle (v) at x2
We can use the work-energy theorem to find the speed of the particle at x2. According to this theorem, the work done by the force on the particle is equal to the change in its kinetic energy.
Work done by the force:
W = ∫F.dx (from x1 to x2)
W = ∫-4/x^2.dx (from 0.04 m to 2 m)
W = [-4x^-1] from 0.04 m to 2 m
W = (-4/2) - (-4/0.04)
W = 198 J
Change in kinetic energy:
ΔK.E. = K.E. at x2 - K.E. at x1
ΔK.E. = (1/2)mv^2 - 0 (initially at rest)
Equating work done and change in kinetic energy:
W = ΔK.E.
198 = (1/2)mv^2
Solving for v:
v = sqrt(396/m)
v = sqrt(396/2)
v = 14.07 m/s
Therefore, the speed of the particle at x2 is 14.07 m/s.
Explanation:
- Given the mass of particle, initial and final position, and force of attraction acting on the particle.
- We used the work-energy theorem to find the speed of the particle at x2.
- According to the theorem, the work done by the force on the particle is equal to the change in its kinetic energy.
- We calculated the work done by integrating the force over the distance from x1 to x2.
- We calculated the change in kinetic energy as the difference between the kinetic energy at x2 and the initial kinetic energy (which is zero as the particle starts from rest).
- Equating work done and change in kinetic energy, we solved for the speed of the particle at x2.
- The final answer is 14.07 m/s.
Given: Mass of particle (m) = 2 kg
Initial position (x1) = 4 cm = 0.04 m
Final position (x2) = 2 m
Force of attraction (F) = -4/x^2
To find: Speed of particle (v) at x2
We can use the work-energy theorem to find the speed of the particle at x2. According to this theorem, the work done by the force on the particle is equal to the change in its kinetic energy.
Work done by the force:
W = ∫F.dx (from x1 to x2)
W = ∫-4/x^2.dx (from 0.04 m to 2 m)
W = [-4x^-1] from 0.04 m to 2 m
W = (-4/2) - (-4/0.04)
W = 198 J
Change in kinetic energy:
ΔK.E. = K.E. at x2 - K.E. at x1
ΔK.E. = (1/2)mv^2 - 0 (initially at rest)
Equating work done and change in kinetic energy:
W = ΔK.E.
198 = (1/2)mv^2
Solving for v:
v = sqrt(396/m)
v = sqrt(396/2)
v = 14.07 m/s
Therefore, the speed of the particle at x2 is 14.07 m/s.
Explanation:
- Given the mass of particle, initial and final position, and force of attraction acting on the particle.
- We used the work-energy theorem to find the speed of the particle at x2.
- According to the theorem, the work done by the force on the particle is equal to the change in its kinetic energy.
- We calculated the work done by integrating the force over the distance from x1 to x2.
- We calculated the change in kinetic energy as the difference between the kinetic energy at x2 and the initial kinetic energy (which is zero as the particle starts from rest).
- Equating work done and change in kinetic energy, we solved for the speed of the particle at x2.
- The final answer is 14.07 m/s.
Community Answer
A particle of mass 2kg is moves on the x-axis under influence of force...
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A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be?
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A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be?.
A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2kg is moves on the x-axis under influence of force of attraction acting towards the origin given by f is equal to minus 4 upon x square if the particle starts from rest at x is equal to 4 cm the speed it will attain to reach the point x is equal to 2 metre will be?.
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