An aluminum clock pendulum having a period of 1.20 s keepsperfect time at 20.0°C

Question

An aluminum clock pendulum having a period of 1.20 s keepsperfect time at 20.0°C. (a) When placed in a room at a temperature of 4°C, will itgain time or lose time? 1 It will gain time. It will lose time.
Your answer is correct.

(b) How much time will it gain or lose every hour? Hint: Seechapter 10. 2 s An aluminum clock pendulum having a period of 1.20 s keepsperfect time at 20.0°C. (a) When placed in a room at a temperature of 4°C, will itgain time or lose time? 1 It will gain time. It will lose time.
Your answer is correct.

(b) How much time will it gain or lose every hour? Hint: Seechapter 10. 2 s

Explanation / Answer

An aluminum clock pendulum having a period of 1.20 s keepsperfect time at 20.0°C. (a) When placed in a room at a temperature of 4°C, will itgain time or lose time? 1 It will gain time. It will lose time.   

T=2l/g where T is the time period of the pendulumclock and l is the length of the pendulum .when the temperature isdecreased the length will decrease . as a result T will decrease.sothe time shown by it will be increased ie the clock will movefast
hence .It will gain time
is the correct option.





(b) How much time will it gain or lose every hour?
length of the pendulum for a period of 1.2sec=0.3578m

coefficient of linear expansion ofaluminum==23*10-6/0C
the length of the pendulum at
4 degree C=0.3578[1-23*10-6(20-4)]=0.3576m
as time period is proportional to length
new time period=l2/l1 *T(old time period)=1.19966sec
so for every oscillation ie for1.2sec the pendulum will gain a timeof
1.2-1.19966=0.00034sec
in one hour there are 3600sec and 3600/1.2=3000 oscillations
hence the gain in time=3000*0.00034=1.02sec



coefficient of linear expansion ofaluminum==23*10-6/0C
the length of the pendulum at
4 degree C=0.3578[1-23*10-6(20-4)]=0.3576m
as time period is proportional to length
new time period=l2/l1 *T(old time period)=1.19966sec
so for every oscillation ie for1.2sec the pendulum will gain a timeof
1.2-1.19966=0.00034sec
in one hour there are 3600sec and 3600/1.2=3000 oscillations
hence the gain in time=3000*0.00034=1.02sec

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