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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)4T/3
- d)T/3
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
Effect of Acceleration on Time Period of Pendulum:
When the lift is stationary, the time period of the simple pendulum is T.
Effect of Acceleration on the Pendulum:
- When the lift accelerates upwards with an acceleration g/3, the effective acceleration acting on the pendulum will be (g + g/3) = 4g/3.
- This effective acceleration will change the time period of the simple pendulum.
Formula for Time Period of a Simple Pendulum:
The formula for the time period of a simple pendulum is given by:
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
Calculating Time Period with Acceleration:
- When the lift accelerates upwards with an acceleration g/3, the effective acceleration acting on the pendulum becomes 4g/3.
- Substituting the new acceleration in the formula, we get:
T' = 2π√(l/(4g/3))
T' = 2π√(3l/4g)
T' = 2π√(3/4)√(l/g)
T' = (π√3/2) √(l/g)
T' = T√3/2
Therefore, the time period of the simple pendulum when the lift accelerates upwards with an acceleration g/3 is T√3/2, which corresponds to option B.
Effect of Acceleration on Time Period of Pendulum:
When the lift is stationary, the time period of the simple pendulum is T.
Effect of Acceleration on the Pendulum:
- When the lift accelerates upwards with an acceleration g/3, the effective acceleration acting on the pendulum will be (g + g/3) = 4g/3.
- This effective acceleration will change the time period of the simple pendulum.
Formula for Time Period of a Simple Pendulum:
The formula for the time period of a simple pendulum is given by:
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
Calculating Time Period with Acceleration:
- When the lift accelerates upwards with an acceleration g/3, the effective acceleration acting on the pendulum becomes 4g/3.
- Substituting the new acceleration in the formula, we get:
T' = 2π√(l/(4g/3))
T' = 2π√(3l/4g)
T' = 2π√(3/4)√(l/g)
T' = (π√3/2) √(l/g)
T' = T√3/2
Therefore, the time period of the simple pendulum when the lift accelerates upwards with an acceleration g/3 is T√3/2, which corresponds to option B.
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