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A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.?
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A particle is in uniform circular motion of time period T such that th...
Given Information:
- Particle is in uniform circular motion with time period T.
- Magnitude of change in velocity vector during T/6 is equal to the magnitude of change in acceleration vector during T/3.
Solution:
Velocity Change:
- The magnitude of change in velocity vector during T/6 is given by Δv = v(T/6) - v(0), where v(t) is the velocity at time t.
- For uniform circular motion, v(t) = ωr, where ω is the angular velocity and r is the radius of the circle.
- Therefore, Δv = ωr - ωr = 0.
Acceleration Change:
- The magnitude of change in acceleration vector during T/3 is given by Δa = a(T/3) - a(0), where a(t) is the acceleration at time t.
- For uniform circular motion, a(t) = ω^2r, where ω is the angular velocity and r is the radius of the circle.
- Therefore, Δa = ω^2r - ω^2r = 0.
Equating the Changes:
- Since the magnitudes of change in velocity and acceleration are equal, we have Δv = Δa.
- This implies 0 = 0, which is true for all values of T.
Conclusion:
- The value of T can be any positive real number.
- Hence, the correct answer is that the value of T in seconds can be any positive real number.
This solution shows that the value of T can be any positive real number, as the magnitudes of change in velocity and acceleration are equal.
- Particle is in uniform circular motion with time period T.
- Magnitude of change in velocity vector during T/6 is equal to the magnitude of change in acceleration vector during T/3.
Solution:
Velocity Change:
- The magnitude of change in velocity vector during T/6 is given by Δv = v(T/6) - v(0), where v(t) is the velocity at time t.
- For uniform circular motion, v(t) = ωr, where ω is the angular velocity and r is the radius of the circle.
- Therefore, Δv = ωr - ωr = 0.
Acceleration Change:
- The magnitude of change in acceleration vector during T/3 is given by Δa = a(T/3) - a(0), where a(t) is the acceleration at time t.
- For uniform circular motion, a(t) = ω^2r, where ω is the angular velocity and r is the radius of the circle.
- Therefore, Δa = ω^2r - ω^2r = 0.
Equating the Changes:
- Since the magnitudes of change in velocity and acceleration are equal, we have Δv = Δa.
- This implies 0 = 0, which is true for all values of T.
Conclusion:
- The value of T can be any positive real number.
- Hence, the correct answer is that the value of T in seconds can be any positive real number.
This solution shows that the value of T can be any positive real number, as the magnitudes of change in velocity and acceleration are equal.
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A particle is in uniform circular motion of time period T such that th...
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A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.?
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A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.? 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 is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.?.
A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.? 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 is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is in uniform circular motion of time period T such that the magnitude of change in 1)velocity vector during T/6 and 2)Acceleration vector during T/3 ate equal. then value of T in seconds. is a) 2π\√3 b) 2√3π c) π\2√3 d) 4π\√3 plz. explain with solutions.?.
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