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If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-?
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If the mass of bob in S simple pendulum is increased to thrice its ori...
Understanding the Simple Pendulum
The time period (T) of a simple pendulum is determined by the formula:
T = 2π√(L/g)
where:
- L = length of the pendulum
- g = acceleration due to gravity
The mass of the bob does not affect the time period.
Original Conditions
- Let the original mass of the bob be m.
- Original length (L1) = L.
- Original time period (T1) = 2π√(L/g).
New Conditions
- New mass of the bob = 3m (mass does not affect T).
- New length (L2) = L/2.
New Time Period Calculation
Using the formula for the time period with the new length:
T2 = 2π√(L2/g)
T2 = 2π√((L/2)/g)
T2 = 2π√(L/(2g))
T2 = 2π√(L/g) * 1/√2
T2 = T1/√2.
Ratio of New to Original Time Period
To find the value of x, we compare T2 with T1:
T2 = T1/√2.
Thus,
x = 1/√2.
Conclusion
The value of x, which represents how the new time period compares to the original time period, is approximately:
x = 0.7071.
This indicates that the new time period is about 70.71% of the original time period.
The time period (T) of a simple pendulum is determined by the formula:
T = 2π√(L/g)
where:
- L = length of the pendulum
- g = acceleration due to gravity
The mass of the bob does not affect the time period.
Original Conditions
- Let the original mass of the bob be m.
- Original length (L1) = L.
- Original time period (T1) = 2π√(L/g).
New Conditions
- New mass of the bob = 3m (mass does not affect T).
- New length (L2) = L/2.
New Time Period Calculation
Using the formula for the time period with the new length:
T2 = 2π√(L2/g)
T2 = 2π√((L/2)/g)
T2 = 2π√(L/(2g))
T2 = 2π√(L/g) * 1/√2
T2 = T1/√2.
Ratio of New to Original Time Period
To find the value of x, we compare T2 with T1:
T2 = T1/√2.
Thus,
x = 1/√2.
Conclusion
The value of x, which represents how the new time period compares to the original time period, is approximately:
x = 0.7071.
This indicates that the new time period is about 70.71% of the original time period.
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If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-?
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If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-?.
If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mass of bob in S simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x times its length time period. then the value of x is :-?.
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