A scientist measures the time period of a simple pendulum as T in a lift at rest. If the lift moves up with a acceleration as one fourth of the acceleration of gravity, the new time period is
Question
A scientist measures the time period of a simple pendulum as T in a lift at rest. If the lift moves up with a acceleration as one fourth of the acceleration of gravity, the new time period is
Solution
The time period of a simple pendulum is given by the formula T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.
When the lift is moving upwards with an acceleration of g/4, the effective acceleration due to gravity in the lift becomes g' = g + g/4 = 5g/4.
Substituting this into the formula for the time period, we get T' = 2π√(l/g') = 2π√(l/(5g/4)) = 2π√(4l/5g).
Comparing this with the original time period T, we can see that T' = T√(4/5).
So, the new time period of the pendulum when the lift is moving upwards with an acceleration of g/4 is T' = T√(4/5).
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