A clock regulated by a seconds pendulum keeps correct time. During summer the length of the pendulum increases to 1.01 m. How much will the clock gain or lose in one day? (g = 9.8 m/s²) (Ans : Lose time 734.4 s)
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Answered by
45
first of all, we have to find time period of pendulum after increament of length.
So, T = 2π√(1.01/9.8) = 2.01607782 sec
But we know, time period of simple pendulum is 2 sec . It means time period increase 0.01607782 sec hence, clock will be slow then it loses time .
So, change in time period , ∆T =0.01607782
one days = 24 × 60 × 60 = 86400 sec
For 2 second there is decrease in = 0.01607782 sec
for 1 sec there is decrease in time = 0.01607782/2 sec
for one days there is decrease in time = 86400 × 0.01607782/2 sec = 694.56 sec
[ Note : actually answer is not matching because of value of π. I used π = 3.14 sec may be here we have to use π = 22/7 , you can use it , for getting exact value ]
So, T = 2π√(1.01/9.8) = 2.01607782 sec
But we know, time period of simple pendulum is 2 sec . It means time period increase 0.01607782 sec hence, clock will be slow then it loses time .
So, change in time period , ∆T =0.01607782
one days = 24 × 60 × 60 = 86400 sec
For 2 second there is decrease in = 0.01607782 sec
for 1 sec there is decrease in time = 0.01607782/2 sec
for one days there is decrease in time = 86400 × 0.01607782/2 sec = 694.56 sec
[ Note : actually answer is not matching because of value of π. I used π = 3.14 sec may be here we have to use π = 22/7 , you can use it , for getting exact value ]
Answered by
7
Answer:734.4 sec per day
Explanation:
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