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If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)
- a)12 Er
- b)16 Ei
- c)8 Er
- d)15 Ei
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the radius of the circular path and frequency of revolution of a ...
Initial kinetic energy of the body,
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Ei = 2π2 mr21f21 ………..(i)
Where, f1 = frequency of revolution of the body.
When, r2 = 2r1 and f2 = and 2f1 , then
Change in kinetic energy,
ΔE = Er -Ei
= 16Ei - Ei = 15 Ei
Most Upvoted Answer
If the radius of the circular path and frequency of revolution of a ...
Change in Kinetic Energy Formula:
The change in kinetic energy (ΔKE) of an object can be calculated using the formula:
ΔKE = KEf - KEi
Where:
ΔKE = Change in kinetic energy
KEf = Final kinetic energy
KEi = Initial kinetic energy
Given Information:
Let's denote the initial radius of the circular path as r and the initial frequency of revolution as f. The mass of the particle is denoted by m.
The problem states that if the radius and frequency are doubled, we need to find the change in kinetic energy.
Initial Kinetic Energy:
The initial kinetic energy of the particle can be calculated using the formula:
KEi = (1/2) m v^2
Where:
v = velocity of the particle
We know that the velocity of a particle moving in a circular path can be calculated using the formula:
v = 2πr f
Where:
r = radius of the circular path
f = frequency of revolution
Substituting this value of v in the initial kinetic energy formula:
KEi = (1/2) m (2πr f)^2
= (1/2) m (4π^2 r^2 f^2)
= 2π^2 m r^2 f^2
Final Kinetic Energy:
Similarly, the final kinetic energy of the particle can be calculated using the formula:
KEf = (1/2) m v'^2
Where:
v' = final velocity of the particle
Since the radius and frequency are doubled, the final velocity can be calculated as:
v' = 2v
= 2(2πr f)
= 4πr f
Substituting this value of v' in the final kinetic energy formula:
KEf = (1/2) m (4πr f)^2
= (1/2) m (16π^2 r^2 f^2)
= 8π^2 m r^2 f^2
Change in Kinetic Energy:
Using the formula for change in kinetic energy:
ΔKE = KEf - KEi
= 8π^2 m r^2 f^2 - 2π^2 m r^2 f^2
= 6π^2 m r^2 f^2
Since we are only interested in the ratio of the final to initial kinetic energy, we can simplify the expression:
ΔKE / KEi = (6π^2 m r^2 f^2) / (2π^2 m r^2 f^2)
= 3
Therefore, the change in kinetic energy is 3 times the initial kinetic energy.
Answer:
Option D) 15 Ei
The change in kinetic energy (ΔKE) of an object can be calculated using the formula:
ΔKE = KEf - KEi
Where:
ΔKE = Change in kinetic energy
KEf = Final kinetic energy
KEi = Initial kinetic energy
Given Information:
Let's denote the initial radius of the circular path as r and the initial frequency of revolution as f. The mass of the particle is denoted by m.
The problem states that if the radius and frequency are doubled, we need to find the change in kinetic energy.
Initial Kinetic Energy:
The initial kinetic energy of the particle can be calculated using the formula:
KEi = (1/2) m v^2
Where:
v = velocity of the particle
We know that the velocity of a particle moving in a circular path can be calculated using the formula:
v = 2πr f
Where:
r = radius of the circular path
f = frequency of revolution
Substituting this value of v in the initial kinetic energy formula:
KEi = (1/2) m (2πr f)^2
= (1/2) m (4π^2 r^2 f^2)
= 2π^2 m r^2 f^2
Final Kinetic Energy:
Similarly, the final kinetic energy of the particle can be calculated using the formula:
KEf = (1/2) m v'^2
Where:
v' = final velocity of the particle
Since the radius and frequency are doubled, the final velocity can be calculated as:
v' = 2v
= 2(2πr f)
= 4πr f
Substituting this value of v' in the final kinetic energy formula:
KEf = (1/2) m (4πr f)^2
= (1/2) m (16π^2 r^2 f^2)
= 8π^2 m r^2 f^2
Change in Kinetic Energy:
Using the formula for change in kinetic energy:
ΔKE = KEf - KEi
= 8π^2 m r^2 f^2 - 2π^2 m r^2 f^2
= 6π^2 m r^2 f^2
Since we are only interested in the ratio of the final to initial kinetic energy, we can simplify the expression:
ΔKE / KEi = (6π^2 m r^2 f^2) / (2π^2 m r^2 f^2)
= 3
Therefore, the change in kinetic energy is 3 times the initial kinetic energy.
Answer:
Option D) 15 Ei
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If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer?
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If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer?.
If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Er are the Initial and final kinetic energies of the particle respectively.)a)12 Erb)16 Eic)8 Erd)15 EiCorrect answer is option 'D'. Can you explain this answer?.
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