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A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]
- a)2π sec
- b)π/2 sec
- c)π sec
- d)(3π/2)sec
Correct answer is option 'C'. Can you explain this answer?
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A body is executing S .H. M . When the displacements from the mean pos...
Understanding Simple Harmonic Motion (SHM)
In SHM, the relationship between displacement, velocity, and time period is crucial for solving problems.
Given Data
- Displacement 1 (x1) = 4 cm, Velocity 1 (v1) = 10 cm/s
- Displacement 2 (x2) = 5 cm, Velocity 2 (v2) = 8 cm/s
Key Equations
The formula for velocity in SHM is given by:
v = ω√(A² - x²)
Where:
- v = velocity
- ω = angular frequency
- A = amplitude
- x = displacement
Applying the Equations
1. For the first displacement:
10 = ω√(A² - 4²) (Equation 1)
2. For the second displacement:
8 = ω√(A² - 5²) (Equation 2)
Squaring the Equations
- From Equation 1:
100 = ω²(A² - 16)
- From Equation 2:
64 = ω²(A² - 25)
Subtracting the Equations
Subtract the second equation from the first:
100 - 64 = ω²[(A² - 16) - (A² - 25)]
36 = ω²(9)
ω² = 4
ω = 2 rad/s
Calculating Time Period (T)
The time period T is related to angular frequency by:
T = 2π/ω
Substituting the value of ω:
T = 2π/2 = π seconds
Conclusion
Thus, the time period of the body executing SHM is:
Correct Answer: (C) π seconds
In SHM, the relationship between displacement, velocity, and time period is crucial for solving problems.
Given Data
- Displacement 1 (x1) = 4 cm, Velocity 1 (v1) = 10 cm/s
- Displacement 2 (x2) = 5 cm, Velocity 2 (v2) = 8 cm/s
Key Equations
The formula for velocity in SHM is given by:
v = ω√(A² - x²)
Where:
- v = velocity
- ω = angular frequency
- A = amplitude
- x = displacement
Applying the Equations
1. For the first displacement:
10 = ω√(A² - 4²) (Equation 1)
2. For the second displacement:
8 = ω√(A² - 5²) (Equation 2)
Squaring the Equations
- From Equation 1:
100 = ω²(A² - 16)
- From Equation 2:
64 = ω²(A² - 25)
Subtracting the Equations
Subtract the second equation from the first:
100 - 64 = ω²[(A² - 16) - (A² - 25)]
36 = ω²(9)
ω² = 4
ω = 2 rad/s
Calculating Time Period (T)
The time period T is related to angular frequency by:
T = 2π/ω
Substituting the value of ω:
T = 2π/2 = π seconds
Conclusion
Thus, the time period of the body executing SHM is:
Correct Answer: (C) π seconds
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A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer?.
A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A body is executing S .H. M . When the displacements from the mean position are 4cm 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 [1991]a)2π secb)π/2 secc)π secd)(3π/2)secCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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