Consider a simple pendulum of length 1.00m suspended from the roof of a lift. While the lift is at rest, the period of small oscillations is carefully measured. Later, while the lift is moving vertically upward with uniform acceleration, the period is found to increase to 1.80s. Assume the value of the acceleration due to gravity in the laboratory to be 9.8ms−2.
(i) Starting from the relation for the period of a simple pendulum, derive an expression for the acceleration due to gravity in terms of its length and measured period.
(ii) Taking the result of part (i) as known, show how the period of a pendulum is affected when it is carried in a lift moving with uniform upward acceleration a.
(iii) Using the observed period 1.80s inside the lift, calculate the magnitude of the lift’s acceleration.