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The time periode of simple pendulum measured inside a stationary lift is found to be T. If the lift starts acclerating upwards with an acceleration g/3, the time periode is
- a)T √3
- b)T √3/2
- c)T √3
- d)T/3
Correct answer is option 'B'. Can you explain this answer?
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Understanding the Simple Pendulum
A simple pendulum's time period (T) is determined by the formula:
T = 2π√(L/g),
where L is the length of the pendulum and g is the acceleration due to gravity.
Effect of Lift's Acceleration
When a lift accelerates upwards with an acceleration of g/3, the effective acceleration due to gravity (g') experienced by the pendulum changes. The effective gravity is the sum of the gravitational force and the lift's acceleration:
g' = g + (g/3) = (4g/3).
New Time Period Calculation
Now, substituting g' into the time period formula gives:
T' = 2π√(L/g') = 2π√(L/(4g/3)).
This simplifies to:
T' = 2π√(3L/4g) = (T/√3)√(3) = T√3/2.
Thus, the new time period T' can be expressed as:
T' = T√3/2.
Final Conclusion
Therefore, when the lift accelerates upwards at g/3, the time period of the simple pendulum becomes:
T' = T√3/2.
The correct answer is option 'B'.
A simple pendulum's time period (T) is determined by the formula:
T = 2π√(L/g),
where L is the length of the pendulum and g is the acceleration due to gravity.
Effect of Lift's Acceleration
When a lift accelerates upwards with an acceleration of g/3, the effective acceleration due to gravity (g') experienced by the pendulum changes. The effective gravity is the sum of the gravitational force and the lift's acceleration:
g' = g + (g/3) = (4g/3).
New Time Period Calculation
Now, substituting g' into the time period formula gives:
T' = 2π√(L/g') = 2π√(L/(4g/3)).
This simplifies to:
T' = 2π√(3L/4g) = (T/√3)√(3) = T√3/2.
Thus, the new time period T' can be expressed as:
T' = T√3/2.
Final Conclusion
Therefore, when the lift accelerates upwards at g/3, the time period of the simple pendulum becomes:
T' = T√3/2.
The correct answer is option 'B'.
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The time periode of simple pendulum measured inside a stationary lift is found to be T. If the lift starts acclerating upwards with an acceleration g/3, the time periode isa)T √3b)T √3/2c)T √3d)T/3Correct answer is option 'B'. Can you explain this answer?
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