Consider clock based on a simple pendulum that is outdoors in Helsinki,Finland.The pendulum consists of a mass of 1.00 kg that is hanging from a thin 3.000-m long aluminum rod.The clock is calibrated perfectly during a summer day with the average temperature of 25^oC.During a winter day with average temperature of -25 $\circ$ C,in a 24-hour period the clock will have measured A)exactly 24.00 hours. B)24 hours and 48 seconds. C)23 hours,59 minutes,and 12 seconds. D)24 hours,1 minute,and 35 seconds. E)23 hours,58 minutes,and 25 seconds.

Question

Quizplus · Accepted Answer

The period of a pendulum (the time it takes to swing back and forth) 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. Since the length of the pendulum remains constant, the period of the pendulum depends only on the value of g, which varies slightly with location and altitude. However, the period of the pendulum also depends on the value of g, which decreases with increasing temperature. Therefore, when the temperature decreases, the period of the pendulum increases and the clock will run slower. According to the formula for the period of a pendulum, we can calculate that the period of the clock during a summer day with an average temperature of 25°C is approximately 2.025 seconds. During a winter day with an average temperature of -25°C, the period of the clock will increase by approximately 0.089 seconds, resulting in a total period of approximately 2.114 seconds. Therefore, in a 24-hour period, the clock will measure approximately 24*60*60/2.114=51379.5 swings of the pendulum, or approximately 24 hours, 1 minute, and 35 seconds. Therefore, the correct answer is D.

Consider Clock Based on a Simple Pendulum That Is Outdoors ∘\circ∘

Consider Clock Based on a Simple Pendulum That Is Outdoors $\circ$