Multiple choice

An accurate pendulum clock is mounted on the ground floor of high building. How much time will it lose or gain in one day if it is transferred to top storey of a building which is h = 200m higher than the ground floor. Radius of earth is 6.4 × 106m.

  1. it will lose 6.2s

  2. it will lose 2.7s

  3. it will gain 5.2s

  4. it will gain 1.6s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The time period of a pendulum is inversely proportional to the square root of the acceleration due to gravity, g. At a height h, the gravity is reduced to g' = g(1 - 2h/R), which increases the time period by a fraction of h/R. Thus, the clock runs slower and loses time equal to 86400 * (h/R) = 86400 * 200 / (6.4 * 10^6) = 2.7 seconds per day.

AI explanation

Using the formula for the change in period of a pendulum with height, the time lost in one day is T multiplied by h divided by R, where T is 86400 seconds, h is 200 meters and R is 6.4 multiplied by 10 to the power of 6 meters. Plugging in the values gives 86400 multiplied by 200 divided by 6400000, which equals 2.7 seconds. The clock will lose 2.7 seconds.

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