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A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body is
- a)2 π/2 sec
- b)π sec
- c)3 π/2 sec
- d)2 π sec
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A body is executing S.H.M When its displacement from the mean position...
v=ω√A2−x2
⇒8=ω √A2−25
&10=ω√A2−16
⇒(8/10)2= A2−25/ A2−16
⇒16/25= A2−25/ A2−16
⇒16A2−256=25A2−625
⇒9A2=369
A2=41
⇒8=ω41−25
⇒8=4ω
∴ω=2=T2π
T=π sec
⇒8=ω √A2−25
&10=ω√A2−16
⇒(8/10)2= A2−25/ A2−16
⇒16/25= A2−25/ A2−16
⇒16A2−256=25A2−625
⇒9A2=369
A2=41
⇒8=ω41−25
⇒8=4ω
∴ω=2=T2π
T=π sec
Most Upvoted Answer
A body is executing S.H.M When its displacement from the mean position...
Given Data:
- Displacement from mean position (x1) = 4 cm, (x2) = 5 cm
- Velocities at x1 (v1) = 10 cm/sec, at x2 (v2) = 8 cm/sec
Formula:
The velocity of a body in Simple Harmonic Motion (S.H.M) is given by v = ω√(A^2 - x^2), where:
- v is the velocity of the body
- ω is the angular frequency of the motion
- A is the amplitude of the motion
- x is the displacement of the body from the mean position
Calculations:
Given v1 = 10 cm/sec and x1 = 4 cm:
10 = ω√(A^2 - 4^2)
100 = ω^2(A^2 - 16) ... (1)
Given v2 = 8 cm/sec and x2 = 5 cm:
8 = ω√(A^2 - 5^2)
64 = ω^2(A^2 - 25) ... (2)
Dividing equation (1) by equation (2):
100/64 = (A^2 - 16)/(A^2 - 25)
25/16 = (A^2 - 16)/(A^2 - 25)
25(A^2 - 25) = 16(A^2 - 16)
25A^2 - 625 = 16A^2 - 256
9A^2 = 369
A^2 = 369/9
A^2 = 41
A ≈ √41
A ≈ 6.4 cm
The time period of a body in S.H.M is given by T = 2π/ω, where ω is the angular frequency.
T = 2π/ω
T = 2π/√(g/A)
T = 2π/√(9.8/6.4)
T = 2π/√1.531
T ≈ 2 sec
Therefore, the time period of the body is 2 seconds (option B).
- Displacement from mean position (x1) = 4 cm, (x2) = 5 cm
- Velocities at x1 (v1) = 10 cm/sec, at x2 (v2) = 8 cm/sec
Formula:
The velocity of a body in Simple Harmonic Motion (S.H.M) is given by v = ω√(A^2 - x^2), where:
- v is the velocity of the body
- ω is the angular frequency of the motion
- A is the amplitude of the motion
- x is the displacement of the body from the mean position
Calculations:
Given v1 = 10 cm/sec and x1 = 4 cm:
10 = ω√(A^2 - 4^2)
100 = ω^2(A^2 - 16) ... (1)
Given v2 = 8 cm/sec and x2 = 5 cm:
8 = ω√(A^2 - 5^2)
64 = ω^2(A^2 - 25) ... (2)
Dividing equation (1) by equation (2):
100/64 = (A^2 - 16)/(A^2 - 25)
25/16 = (A^2 - 16)/(A^2 - 25)
25(A^2 - 25) = 16(A^2 - 16)
25A^2 - 625 = 16A^2 - 256
9A^2 = 369
A^2 = 369/9
A^2 = 41
A ≈ √41
A ≈ 6.4 cm
The time period of a body in S.H.M is given by T = 2π/ω, where ω is the angular frequency.
T = 2π/ω
T = 2π/√(g/A)
T = 2π/√(9.8/6.4)
T = 2π/√1.531
T ≈ 2 sec
Therefore, the time period of the body is 2 seconds (option B).
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A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer?
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A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer?.
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A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A body is executing S.H.M When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body isa)2π/2secb)πsecc)3π/2secd)2π secCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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